Notes

Abstract:

This research presents hardware and software solutions to many of the problems facing biological solid state nuclear magnetic resonance (ssNMR) spectroscopy at high fields. The low-E 750 MHz magic angle spinning (MAS) probe was designed, constructed, and thoroughly characterized. Under normal operating conditions, a proton (hydrogen, isotope weight 1) RF field nutation rate of 93 kHz and homogeneity (810 degrees/90 degrees) of 93% can be obtained with a sample length of 8.4 mm corresponding to a volume of 80 uL. With a higher power amplifier, we should be able to exceed 110 kHz decoupling fields based on bench measurements. Carbon (isotope weight 13) RF field nutation rates greater than 70 kHz with a homogeneity (810 degrees/90 degrees) of 70% are routinely observed for this sample length; the carbon RF homogeneity can be increased to 89% with a 6.7 mm sample length. Under full proton decoupling for long periods of time, sample heating due to the high RF field is minimal even for samples containing physiological levels of salt. We have not noticed any sample degradation in heat sensitive samples after extensive experimentation. The power handling characteristics, RF fields, and homogeneities make this an ideal probe for applying the full range of MAS solid state NMR experiments, including sequences which use extended periods of continuous RF pulsing on both channels, to biological samples which are inherently dilute. A system for optimizing pulse sequences for ssNMR was also developed, demonstrated, and is running. This system was demonstrated on the two standard pulse sequences used to test pulse optimization systems: the inversion experiment and the refocusing experiment. In both cases, pulse sequences were derived which had a wider bandwidth than existing pulse sequences and had extremely good agreement between experiment and simulation. These pulse sequences should be useful in maintaining high signal strength and phase coherence in future research. The methods of optimization and verification allow them to be easily extended to more complex situations in future research. The combination of the new probe and the method for optimizing pulse sequences for use at higher fields opens many opportunities for new research on biological solids.

General Note:

In the series University of Florida Digital Collections.

General Note:

Includes vita.

Bibliography:

Includes bibliographical references.

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Description based on online resource; title from PDF title page.

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This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.

Statement of Responsibility:

by Seth Mcneill.

Thesis:

Thesis (Ph.D.)--University of Florida, 2009.

Local:

Adviser: Arroyo, Amauri A.

Local:

Co-adviser: Long, Joanna R.

Electronic Access:

RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2010-05-31

Notes

Abstract:

This research presents hardware and software solutions to many of the problems facing biological solid state nuclear magnetic resonance (ssNMR) spectroscopy at high fields. The low-E 750 MHz magic angle spinning (MAS) probe was designed, constructed, and thoroughly characterized. Under normal operating conditions, a proton (hydrogen, isotope weight 1) RF field nutation rate of 93 kHz and homogeneity (810 degrees/90 degrees) of 93% can be obtained with a sample length of 8.4 mm corresponding to a volume of 80 uL. With a higher power amplifier, we should be able to exceed 110 kHz decoupling fields based on bench measurements. Carbon (isotope weight 13) RF field nutation rates greater than 70 kHz with a homogeneity (810 degrees/90 degrees) of 70% are routinely observed for this sample length; the carbon RF homogeneity can be increased to 89% with a 6.7 mm sample length. Under full proton decoupling for long periods of time, sample heating due to the high RF field is minimal even for samples containing physiological levels of salt. We have not noticed any sample degradation in heat sensitive samples after extensive experimentation. The power handling characteristics, RF fields, and homogeneities make this an ideal probe for applying the full range of MAS solid state NMR experiments, including sequences which use extended periods of continuous RF pulsing on both channels, to biological samples which are inherently dilute. A system for optimizing pulse sequences for ssNMR was also developed, demonstrated, and is running. This system was demonstrated on the two standard pulse sequences used to test pulse optimization systems: the inversion experiment and the refocusing experiment. In both cases, pulse sequences were derived which had a wider bandwidth than existing pulse sequences and had extremely good agreement between experiment and simulation. These pulse sequences should be useful in maintaining high signal strength and phase coherence in future research. The methods of optimization and verification allow them to be easily extended to more complex situations in future research. The combination of the new probe and the method for optimizing pulse sequences for use at higher fields opens many opportunities for new research on biological solids.

General Note:

In the series University of Florida Digital Collections.

General Note:

Includes vita.

Bibliography:

Includes bibliographical references.

Source of Description:

Description based on online resource; title from PDF title page.

Source of Description:

This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.

Statement of Responsibility:

by Seth Mcneill.

Thesis:

Thesis (Ph.D.)--University of Florida, 2009.

Local:

Adviser: Arroyo, Amauri A.

Local:

Co-adviser: Long, Joanna R.

Electronic Access:

RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2010-05-31

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1 OPTIMIZATION OF HARD WARE AND SOFTWARE FO R SOLID STATE NUCLEA R MAGNETIC RESONANCE A T HIGH MAGNETIC FIEL DS By SETH ALAN MCNEILL A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2009

4 ACKNOWLEDGMENTS I take this opportunity to express sincere gratitude to my advisors, Dr. Joanna R. Long and Dr. A. Antonio Arroyo for providing me with a unique interdisciplinary academic situ ation for acquiring this degree. Dr. Longs uncanny knowledge of nearly everything is both disturbing and inspiring to say the least, and Dr. Arroyos mentoring has made an indelible impact on me throughout my tenure at UF. It was not always easy to coordi nate between schools, but these great individuals have always managed to work things out. I am also thankful to my other committee members, Dr. Haniph A. Latchman, Dr. J. Cole Smith, and Dr. Eric Schwartz for being very supportive over the years. My resea rch was not only financially supported in part by the National High Magnetic Field Laboratory in Tallahassee, FL, but many individuals there contributed greatly to my research. In particular Dr. Peter L. Gorkov, who makes the most beautiful NMR probes in the world, has taught me some excellent techniques. His ability to design and his desire for perfection were a great inspiration to me. Warm thanks are extended to Dr. William W. Brey who provided much training and insight into RF testing and with whom I h ad many good discussions of science and engineering. Special thanks to Kiran Shetty, Jason Kitchen and Ashley Blue for providing tips on construction and help for finding the parts that I needed, and also for helping with NMR experiments in Tallahassee. H ere in Gainesville, I thank the AMRIS staff for keeping the spectrometers going and providing a place for my research. I thank Dr. Daniel Plant in particular for trusting me to reconfigure the magnets every time I get on, and for helping me get good data f rom a marginally installed system. I also thank James R. Rocca for always taking the time to teach me when I had questions.

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5 Throughout my career in the McKnight Brain Institute, the Computer and Information Technology Services guys have always been helpful, even if the service request was ludicrous. The crew at UFs High -Performance Computing Center was always helpful whenever I did calculations over there, especially Jon Akers who managed to provide help both at the MBI and HPC. A great deal of thanks to Shannon Chillingworth, the ECE Academic Services Coordinator who did an amazing job keeping everything straight for me from my late application through many winding paths until I have reached this point. In the Biochemi stry and Molecular Biology office, I thank Regina Corns for managing to keep me paid and my name in all the right spaces for everything to work out even though things (including me) were not always easy to work with or simple. Thanks also go to Denise Mesa and Bradley Moore for doing a wonderful job of keep ing all the odds and ends of me being here in line. The combined Long and Edison labs have provided a very stimulating and wonderfully distracting environment for me to work in throughout the years. My c hurch family at the Gainesville Seventh -day Adventist church has provided a tremendous nurturing environment during my tenure here. The people there have taken a keen interest in me and my academic journey, which has kept me on the straight and narrow. Pas tor Dan Graham has been a great pastor, mentor, friend, and fellow struggler on the path to a PhD. Dr. OJ Ganesh has provided much insight into science, computing, and a host of other things since I see him at lab and church and social functions! Hopefully Katia (his wife) will forgive me for having seen more of him than she did during his tenure in the lab. Thanks go to Dr. Joel Schipper and soon to be Dr. Lavi Zamstein for providing the best rooming situation at the best price in Gainesville for 3 years. It has been a great journey as

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6 Arroyos trio of PhD students. Thanks also go to Dr. Brian Roth who commiserated with and encouraged me from the other side of the country as we pursued our degrees. Deep and heartfelt thanks go to my family who have been ve ry encouraging and helpful throughout my life. My parents instilled curiosity and a belief that I could accomplish anything and go anywhere, which when mediated by a strong belief in God has led me to all kinds of interesting places, including here. Two of my brothers and I constantly commiserate as we are all pursuing PhDs. Our oldest brother and his family provide stability and encouragement from the real world, as well as fun discussions and great nieces. My future in -laws have adopted me in early and be en extremely supportive. In particular, stern words of encouragement my fiances mom has helped to keep me going. My wonderful and beautiful fiance, Corraine, has been through quite a bit with this degree and is definitely looking forward to its comple tion. She has really kept me on track, focused on what needed doing, and encouraged me when the going got tough. Thank you so very much! Most of all, I thank God for giving me life, purpose, and passion throughout everything.

15 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy OPTIMIZATION OF HARD WARE AND SOFTWARE FO R SOLID STATE NUCLEA R MAGNETIC RESONANCE A T HIGH MAGNETIC FIEL DS By Seth Alan McNeill May 2009 Chair: A. Antonio Arroyo Cochair: Joanna R. Long Major: Electrical and Computer Engineering This research presents hardware and software solutions to many of the problems facing biological solid state nuclear magnetic resonance (ssNMR) spectroscopy at high fields. The low E 750 MHz magic angle spinning (MAS) probe was designed, constructed, and t horoughly characterized. Under normal operating conditions, a proton (hydrogen, isotope weight 1) RF field nutation rate of 93 kHz and homogeneity (810 degrees/90 degrees) of 93% can be obtained with a sample length of 8.4 mm corresponding to a volume of 8 0 u L With a higher power amplifier, we should be able to exceed 110 kHz decoupling fields based on bench measurements. Carbon (isotope weight 13) RF field nutation rates greater than 70 kHz with a homogeneity (810 degrees/90 degrees) of 70% are routinely observed for this sample length; the carbon RF homogeneity can be increased to 89% with a 6.7 mm sample length. Under full proton decoupling for long periods of time, sample heating due to the high RF field is minimal even for samples containing physiologi cal levels of salt. We have not noticed any sample degradation in heat sensitive samples after extensive experimentation. The power handling characteristics, RF fields, and homogeneities make this an ideal probe for applying the full range of MAS solid sta te

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16 NMR experiments, including sequences which use extended periods of continuous RF pulsing on both channels, to biological samples which are inherently dilute. A system for optimizing pulse sequences for ssNMR was also developed, demonstrated, and is run ning. This system was demonstrated on the two standard pulse sequences used to test pulse optimization systems: the inversion experiment and the refocusing experiment. In both cases, pulse sequences were derived which had a wider bandwidth than existing pu lse sequences and had extremely good agreement between experiment and simulation. These pulse sequences should be useful in maintaining high signal strength and phase coherence in future research. The methods of optimization and verification allow them to be easily extended to more complex situations in future research.. The combination of the new probe and the method for optimizing pulse sequences for use at higher fields opens many opportunities for new research on biological solids.

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17 CHAPTER 1 INTRODUCTION Nuclear Magnetic Resonance (NMR) Nuclear magnetic resonance (NMR) spectroscopy is a method for determining details of molecular structure and dynamics by exploiting the intrinsic nuclear angular momentum referred to as spin. NMR can be used to investigate the distance between atoms both t hrough space at an atomic (angstrom) scale using dipolar couplings, Figure 1 1, and through chemical bonds using scalar couplings, Figure 1 2. Structural NMR experiments measure the distance between atoms and/or the chemical connectivity between the atoms in order to derive the 3D structures of molecules, particularly biomolecules such as proteins. When the density of signal is measured spatially, it is called nuclear magnetic resonance imaging or MRI. NMR and X -ray crystallography are currently the standar d methods for determining the 3D structure of biomolecules. All nuclei have an intrinsic property known as their spin quantum number. Spin quantum numbers can be positive or negative in multiples of and are usually designated by the letter I. Nuclei wit h a spin number of zero, I = 0, are not NMR active. However, nuclei with I not equal to zero are NMR active since spin angular momentum leads to spin polarization in a magnetic field. The two nuclei of particular interest in this research are 1H and 13C, b oth of which have a spin number of In the presence of a static magnetic field, designated as B0, the magnetic moments lead to energy level differences for the different spin states. For a spin number I, there are 2I + 1 states, so for the spin nuclei we are interested in there are 2 energy levels, usually referred to as and The energy difference between these two states is proportional to B0 with traditionally being the higher energy state and being the lower energy state. Using classical mech anics to describe the effect B0 has on the magnetic moment gives rise to the moment

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18 precessing around the applied magnetic field, B0, like a gyroscope in a gravitational field. The rate of this precession is shown in Equation 11 with units of rad/s and is known as the Larmor frequency of the nucleus. B0 (1 1) The quantity, is known as the gyromagnetic ratio or the magnetogyric ratio and is specific to a type of nucleus. The gyromagnetic ratio of 1H is 267.552 x 106 rad/(s T) and for 13C is 67.283 x 106 rad/(s T) [1]. For a magnetic field of 17.6 T, this gives a Larmor frequency ( /2 ) of 750 MHz for 1H and 188 MHz for 13C. This can be related to the energy difference between the two quantum states, and as given in Equation 1 2. E h2 hB02 (1 2) The constant h is Planks constant. We can use this energy difference to calculate the proportion of spins in the t wo states at a given field using the Boltzmann distribution, Equation 1 3, where N are the number of spins in each state, kB is Boltzmanns constant, and T is absolute temperature. NN e E kBT (1 3) Due to the state being lower energy, ther e will be an excess of spins in that state. To get an idea of the magnitude of the signal we are looking at, the proportion of low energy to high energy spins at 17.6 T is 1.00012 for 1H and 1.00003 for 13C. Thus NMR is traditionally viewed as a low sensit ivity technique relative to X -ray or UV spectroscopy. The ratio of excess spins can be manipulated by irradiating the sample at its resonant frequency, the Larmor frequency. Magnetic fields applied at this frequency can excite the spins

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19 to switch state. Wh en the application is stopped, the spins relax back to their steady state, emitting RF energy in the process. This energy is the signal received in NMR spectroscopy. The RF energy applied to the sample can be pulsed to gain more control of the excitation process and therefore the signal received as the spins relax back to their steady state. These pulses are referred to as the pulse sequence, which is the topic of Chapters 3 and 4. The Larmor frequency of a spin is dependent on the magnetic field experience d by a spin. The static magnetic field induces currents in the electrons around the spin, which creates an opposing magnetic field. The induced current may not produce an exactly opposing magnetic field due to the physical constraints of the structure of t he molecule. This is referred to as chemical shielding. The induced magnetic field shifts the Larmor frequency of nearby spins by a small amount, and this is commonly referred to as chemical shift. The chemical shift is dependent on the bonding arrangement within the molecule, which means it can be useful in determining the chemical environment of an atom and how it is bonded to other atoms. Since the induced magnetic field is dependent on the static magnetic field, the chemical shift is linearly dependent on the strength of the static magnetic field, B0. To allow direct comparison of spectra taken at two different magnetic fields, the chemical shift is usually divided by the Larmor frequency of the magnet in MHz, giving units of parts per million (ppm) rath er than Hertz. The chemical shift of 13C can span up to 200 ppm for biological samples, which translates to 25 kHz for a 500 MHz magnet and 37.5 kHz for a 750 MHz magnet. The chemical shift is also dependent on the orientation of the molecule relative to B0. These spatial dependencies broaden the signals of interest due to multiple molecular orientations in a given sample, reducing resolution and lowering signal sensitivity. The spread of chemical shifts due to this spatial dependency is referred to as chem ical shift anisotropy (CSA). However,

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20 in liquids, the isotropic tumbling of the molecules faster than the NMR time scale averages the different orientations to produce a single sharp peak at the average chemical shift of a spin in a molecule. Thus liquids show no CSA. Equation 1 1 gives the Larmor frequency of a spin due to an external static magnetic field. Each nucleus has a magnetic moment. This moment not only reacts to the static magnetic field, B0, but also is itself a magnetic dipole. The magnetic di poles from different spins interact and affect each others magnetic environment, shifting each others Larmor frequency a little. Therefore, the Larmor frequency of a given species (13C for instance) can shift depending on what other spins are nearby and how far away they are. The dipolar coupling constant, bjk, between spins Ij and Ik is given in Equation 1 4. bjk 04 jk h rjk 3 (1 4) In Equation 1 4, 0 is the magnetic permeability of free space (4 x 107 H/m), h -bar is Plancks constant divided by 2 and rjk is the distance between the two spins. Only known constants and the distance between the two spins determine the dipolar coupling. Therefore, if the dipolar coupling constant can be determined, the distance between two atoms in a molecule can be determined. It is useful to note that the dipolar coupling constant is not dependent on the magnetic field strength, B0. Solid State NMR Conventional NMR is done on molecules dissolved in a liquid. However, there is increasing interest in doing NMR spec troscopy on biological (and other) molecules that are not readily solubilized. NMR spectroscopy on such samples is referred to as solid -state NMR (ssNMR). ssNMR is considerably more complicated than liquid state NMR since the molecules are no longer tumbli ng isotropically on the timescales inherent to the experiments; therefore, the

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21 orientation dependent components of the CSA and dipolar interactions are no longer averaged. These spatial dependencies broaden the signals of interest reducing resolution and l owering signal sensitivity, Figure 1 3. A goal of ssNMR research is to develop techniques to recover the resolution while taking advantage of the added information available from the orientation dependent interactions. One technique frequently employed is to mechanically rotate the samples at very high speeds (5 70 kHz) at a very carefully set angle (the magic angle) with respect to the static magnetic field to mimic isotropic averaging. This technique takes advantage of the fact that the spatial component of many NMR interactions have the form of a second order Legendre polynomial, namely (3cos2 1) where is the angle relative to the static magnetic field. This goes to 0 at arctan(sqrt(2)) which has solutions at ~54.74 and ~125.26. Most magic angle s pinning (MAS) NMR is done at the angle ~54.74. Challenges in NMR There are several challenges in NMR: sensitivity, off resonance, inhomogeneity, and biological samples. Sensitivity As was mentioned earlier, NMR is not a sensitive spectrographic method. There are several methods which attempt to improve the sensitivity. The first method is to use stronger static magnetic fields. Equations 1 2 and 13 show that the proportion of polarized spins increases as the magnetic field increases. The second method i s to use more concentrated samples, and the third method is to use smaller detection coils. Stronger static magnetic fields Higher static magnetic fields are becoming more and more readily available. The push for higher magnetic fields is driven by the fac t that polarization enhancement goes up as B0 7/4,

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22 thereby decreasing acquisition times by a factor of B0 7/2 allowing for either shorter acquisition times or detection of more dilute samples. Experiment time reduction allows for more experiments to be done per unit time and for less magnet time that has to be paid for. Detection of more dilute samples is very important in biological studies since many samples of interest are natively in a dilute setting, difficult to isolate, or difficult to acquire. For ss NMR, increasing the static magnetic field increases the anisotropic chemical shifts (CSAs). These contain important information about the spins of interest. Wider CSAs make differentiating and measuring the CSAs easier, therefore, leading to higher quality measurements. These benefits come with challenges. Higher field magnets are typically less stable than lower field magnets, particularly when they are also wide bore. This implies that every time an experiment is started, all the parameters for the experi ment need to be reoptimized. It is also important to check that the transmitter is still on resonance since magnet frequency (or field strength) drift is much higher on high field magnets. Higher field magnets cost more and so are often shared between dif ferent users. Scheduling and maintenance can become problems as well. Switching between imaging, liquids, and ssNMR provides more opportunity for equipment failures. The higher frequencies that stronger magnets provide also prove to be more challenging fr om an RF standpoint on several fronts. Higher fields require much more care in RF design since small changes in size and/or placement of parts can be a significant part of a wavelength different, causing unexpected/unplanned changes in the RF path. In buil ding the coil system in a probe, one has to be careful of the fact that the length of wire in a coil approaches significant portions of a wavelength. This can lead to standing waves which create very bad homogeneity.

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23 Concentrated samples A seemingly logica l solution to a lack of signal is to pack more sample into the spectrometer by increasing the sample concentration. This works well for one subset of samples. Some samples are not conducive to high concentrations and some experiments require dilute samples to be relevant. Smaller detection coils The sensitivity per unit volume for a solenoidal coil varies as 1/ d where d is the diameter of the coil [2,3] Thus, sensiti vity is improved for smaller diameter coils. Therefore, for samples that can be concentrated, the coil size should be minimized. Off-Resonance In a sample with only one spin, 1H in water for instance, one would not have to worry too much about off -resonan ce effects since it could be excited exactly on resonance. Most biological samples of interest, particularly when looking at the 13C spectra, have multiple spins that differ in chemical shift by up to 200 ppm as mentioned earlier. Chemical shift is proport ional to B0, so this translates to 25 kHz for a 500 MHz magnet and 37.5 kHz for a 750 MHz magnet. For 19F or inorganic compounds, this width can be substantially larger. Most NMR pulse sequences assume that the RF pulses are transmitted at the resonant frequency of the spin of interest. As can be seen, this means that many kHz of bandwidth has to be uniformly excited if the whole spectrum is to be observed. A real pulse does not evenly excite at all frequencies. This means that spins further from resonance experience a different pulse from those on resonance, which can make comparisons across a wide spectrum difficult and prone to problems. Higher power pulses can be used to excite spins more uniformly across frequency offsets, but physical constraints limit the amount of power that can be applied, Figure 1 4.

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24 The best methods to fix this challenge seem to be carefully designed pulse sequences that use composite pulses to bring all spins to the desired polarization at the end. Unfortunately, these tend to be longer than simple hard pulses. This extra irradiation time can be problematic when sample overheating is a concern. This extra time can also be a problem when working with MAS ssNMR. If irradiation is too long, MAS synchronization is lost, thereby jeopardizing the selective reinstatement of desired signals due to the many variables involved and non-analytic solutions. This area of research can benefit from the use of computational optimization of pulse sequences to find pulse sequences, which take less tim e and/or less power to achieve wide bandwidth excitation. This topic is the subject of Chapters 3 and 4. Inhomogeneity Inhomogeneity of the applied RF signal, B1, is a major challenge in ssNMR. B1 homogeneity is determined by the relationship of the sample to the RF coils through which the excitation magnetization is introduced. The geometry of the sample affects the B1 homogeneity. For a solenoidal coil, the highest homogeneity is in the center of the coil, with the field strength diminishing away from the center. Maximum homogeneity of the B1 field is achieved if the sample is restricted to the very center of the coil. This is usually achieved by placing spacers on either side of the sample in the rotor (for ssNMR). The coil geometry also affects the B1 field homogeneity. There has been much research on this topic lately and much improvement This topic will be covered in greater detail in Chapter 2 on hardware development. A simple example is to think about a solenoid. If a solenoid is infinitely long, the magnetic field inside is completely homogeneous down the length of the solenoid. However, due to physical constraints, the coils in probes are of finite lengths. This means that the field strength near the ends of the coil is less than that in the cen ter. If a sample is inside a longer coil, the homogeneity will be better than if the sample is inside a shorter coil.

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25 There are other geometries that play tricks with this idea to improve the homogeneity that will be covered in Chapter 2. The length of wir e used in a coil can also affect homogeneity. As the electrical length of a coil approaches the wavelength of the signal being used, standing waves are setup in the coil, creating nodes of zero current where there is no magnetic field created to excite the sample. Inhomogeneity affects experiments in several ways. The first way is that different parts of the sample experience different RF fields. This makes them nutate at different rates, which reduces the efficiency of experiments, particularly long, windowless, double -quantum recoupling experiments that rely on long trains of pulses. If all the pulses vary by a small amount in parts of the sample, destructive interference sets up and signal is lost. A second way that inhomogeneity affects experiments is i n received signal strength. The receiver sensitivity is proportional to the homogeneity of the field [4]. Biological Samples Biological ssNMR provides its own set of challenges. For sa mples that are not concentration limited, the maximum S/N is achieved by using the smallest sample and smallest RF coil as possible. Unfortunately, samples like this are rarely at physiologically relevant conditions. To be physiologically relevant, many pr oteins (membrane bound ones for example) are concentration limited because have to be in a very dilute environment. For concentration limited cases, a larger overall sample volume gives better S/N [2]. Biological ssNMR also has the challenge of sample heating. In order to be biologically relevant, samples need to be kept at ambient temperatures. Sample temperatures increase due to RF heating, which can degrade a sample. Anoth er form of sample heating is from the magic angle spinning. The air friction on the outside of the rotor (the surface speeds of which can

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26 approach the speed of sound in some cases) can heat the sample by up to 40 C, enough to denature a sample. Goals of T his Research There are two main goals for this research. The first goal is to build and characterize ssNMR probe for high static magnetic field optimized for biological samples by having high homogeneity on both RF channels, high sensitivity for dilute sam ples through a larger sample volume and low RF heating via a unique probe design. The second goal is to optimize pulse sequences to mitigate the issues associated with the expanded chemical shift and CSA experienced at high fields.

28 Figure 1 3. Comparison of a liquid signal to a powder pattern via simulation. The liquid peak is the average of all the orientations while the powder pattern shows the orientation dependent chemical shift anisotropy.

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29 Figure 1 4. High power versus low power excitation. A low power pulse excites spins over a narrow range of frequencies, while a high power pulse excites spins over a wide range of frequencies.

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30 CHAPTER 2 HARDWARE OPTIMIZATIO N Improvements and Challenges at Higher Fields The hardware used in NMR spectroscopy has improved greatly since NMR signals were first observed in the 1940s. In particular, the strength, homogeneity, and stability of magnetic fields has greatly increased, thereby increasing the sensitivity of NMR. This increase in sensitivity broadens the applicability of NMR to include more complex biological systems, particularly for ssNMR techniques. This is important because at a fundamental level NMR is a very insensitive method of spectroscopy since it is detecting very small changes in the sample. Polarization enhancement estimates suggest the increase in signal to noise (S/N) should be on the order of B0 7/4, decreasing acquisition times by a f actor of B0 7/2, which means that increasing the magnetic field from 11.7 T (500 MHz) to 17.6 T (750 MHz) can increase the S/N by about 2.2 times and reduce the amount of experiment time by half or more. The reduction in experiment time means that samples w hich are less stable or that have less signal can be studied. Performing NMR experiments at high magnetic fields, therefore, increases their applicability to systems that are sensitivity limited. It also aids the study of samples that are resolution limit ed. With the advent of stable high field instruments with proton frequencies of 700 to over 900 MHz, the application of solid state NMR (ssNMR) spectroscopy to a wide variety of biomolecular systems has become increasingly feasible. However, realizing thes e sensitivity gains for a variety of samples, nuclei, and pulsed experiments is not straightforward since the increase in signal is accompanied by an increase in the isotropic and anisotropic chemical shifts, Figure 2 1. This results in increased spectral This chapter is largely adapted from: Journal of Magnetic Resonance, doi:10.1016/j.jmr.2008.12.008, Seth A. McNeill, Peter L. Gorkov, Kiran Shetty, William W. Brey and Joanna R. Long, A low E magic angle spinning probe for biological solid state NMR at 750 MHz, 2008, with permission from Elsevier License Number 2110240542593

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31 widths, requiring the generation of more powerful B1 fields to excite all frequencies of interest. Additionally, as at lower magnetic fields, many ssNMR experiments require proton decoupling with RF field strengths above ( 1 kHz on the proton cha nnel for optimal resolution. The Challenge of Radio Frequency Coils at High Frequencies With traditional ssNMR probe circuits utilizing multiply -resonant solenoidal coils, achieving efficient and homogeneous B1 fields is complicated by the electrical leng th of the sample coil at high proton frequency approaching the quarter wavelength limit [5]. Additionally, the study of biomolecules under physiologically relevant conditions substanti ally alters the probe performance by loading the coil with samples containing high salt concentrations. Creating stronger B1 fields also creates stronger electric (E) fields within the sample leading to more heating and, ultimately, sample degradation. The generation of E fields and their contributions to sample heating in ssNMR spectroscopy have been extensively studied in recent years [6 18] This heating can be overcome by cooling samples down to where the heating does not disrupt the system [6], but often this means cooling the samples well below biologically relevant temperatures to where protein conformations are altered or the molecular dynamics of interest are removed. Lowering the conductivity of the samples is another method of reducing heating [7]. This is possible for some samples, but again may lead away from biologically relevant conditions. Common spectroscopic approaches to minimizing sample heating include the use of very low duty cycles and utilizing very small coils, with a subsequent reduction in scans per unit time and sample volume, respectiv ely, leading to poorer S/N and/or longer acquisition times, particularly for concentration limited samples. More recently, probe design efforts have focused on the more fundamental issue of modifying the coil design to reduce sample heating by reducing in ductance and adding shielding.

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32 Traditional multinuclear ssNMR probe designs employ a single, multiply resonant solenoid as this maximizes the filling factor for the various frequencies and (when wavelength effects can be neglected) helps ensure RF overlap. Several clever modifications to the solenoid have been proposed to reduce heating while preserving as much as possible the efficiency of both high and low frequency channels. These designs also allow commercial probe suppliers to continue to use their well -developed multichannel matching networks. Scroll coils [19] (also known as Swiss Rolls) offer a robust solution to the problem of sample heating as they have a lower inductance than solenoids and their geometry creates a built in Faraday shield for the E field since the inner turns shield the sample from the E field generated by the outer turns [8,19] Both these factors reduce sample heating and improve stability and performance on the proton channel. The 1H efficiency of scroll coils with lossy samples can surpass that of solenoids. However, scroll coils are less effici ent than solenoidal coils at lower frequencies due to their low inductance and low Q [8]. Scroll coils also present challenges due to temperature dependent tuning changes in herent to the large capacitance between turns [9,10] this capacitance also limits the available sample volume [18] The Z -coil, consisting of a central loop with two spiral coils on the ends of the loop [11] lowers sample heating by more than an order of magnitude relative to a solenoidal coil as well as having an RF efficiency that is independent of sample conductivity. However, unlike the scroll, the RF efficiency of the Z -coil with a lossy sample is just c omparable to that of the solenoid, and there is also a penalty in sensitivity and efficiency at the lower frequencies. Most recently, Krahn and co -workers have shown that inserting a conductive shield between the sample and the solenoid can reduce the heat ing [12] Precise manufacturing of the shield led to an effective decrease in heating at a modest cost in sensitivity due to the decrease in sample filling factor compared t o an unshielded solenoid. However, the close proximity of the shield to

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33 the sample coil can be expected to limit the voltages, and hence the achievable B1, for larger samples. These three single -coil alternatives to the solenoid have been shown to reduce h eating at some cost to RF efficiency. While the gains in RF and temperature stability certainly outweigh the loss in sensitivity for lossy samples, an alternative approach which does not compromise the sensitivity and efficiency of the lower frequencies wo uld be attractive, particularly since the bulk of biological ssNMR experiments rely on direct detection of low gamma nuclei due to proton resolution limitations at slow to intermediate magic angle spinning speeds. One such solution to improve RF performa nce at the proton frequency and simultaneously reduce sample heating is to use separate coils for the low and high frequencies. There are several benefits to this design: using two coils allows the individual circuits and coils to be optimized for each fre quency range; having one coil inside the other allows the inner coil to act as a partial Faraday shield for the outer coil; the RF fields generated by the two coils can be designed to be orthogonal, which increases channel isolation and therefore efficienc y; and, when the coil assembly is rotated for magic angle applications, the use of orthogonal coils results in a compromised RF field on only one coil. An advantageous approach for using crossed coils in MAS probes is to place a low inductance, segmented 1H saddle coil inside a solenoid tuned for the lower frequency channel [9]. With this configuration, the 1H coil shields the sample from some of the E fields created by the i nductance of the solenoid, improving the low -frequency efficiency in the presence of lossy samples. The inverse configuration, in which the low frequency sensitivity is improved by placing a solenoid within a loop gap resonator (LGR), has been used effecti vely to reduce heating in large volume static probes [18] and is the focus of this project.

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34 The Low -E Solution The LGR is a coil geometry which works well at proton frequenc ies due to its low inductance, lower E fields, and short electrical length; LGRs have been used extensively in EPR for high frequency applications [20] as well as in MRI [21] Previously, we have shown that they also work well for high field static ssNMR applications when combined with an orthogonal solenoid for the lower gamma nuclei [18] a design christened low E due to its favorable mitigation of E fields within the sample space. In such designs, the sample is placed within a solenoidal coil to maximize sensitivity and homogeneity for the low frequency channel; an LGR optimized for the proton channel is orthogonal to and surrounds the solenoid. In this configuration, the solenoid further lowers the E field by acting as a partial Faraday shield between the sample and the LGR. The out er 1H resonator is slit strategically to cancel low frequency eddy currents, which would otherwise reduce the efficiency of the inner coil. The loss of filling factor for the proton channel in a crossed coil setup like this is largely made up for by the im proved efficiency of the single -frequency 1H matching network. Since the solenoid is not called upon to produce a 1H field, its length and number of turns can be increased to improve sensitivity. For a MAS probe, the fact that the field of the LGR can be m ade orthogonal to the polarizing magnetic field, B0, further improves 1H efficiency relative to a multiply tuned solenoid. An additional benefit of the LGR 1H coil is that its homogeneity is excellent. The high B1 homogeneity on both channels of the 1H LGR /13C solenoid configuration is of critical importance for the application of cross -polarization (CP) and multipulse experiments to samples that are concentration limited. In multipulse recoupling experiments, especially long windowless experiments, the acc umulation of phase errors from different parts of the sample nutating at different rates leads to reduced excitation efficiencies and phase errors in the resulting signals,

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35 Figure 2 2. The increased homogeneity of the LGR at the proton frequency and the so lenoidal coil at lower frequencies can increase the efficiency and final signal strength of multipulse experiments, particularly experiments that utilize double quantum filtering. In considering concentration-limited samples, the 1H LGR/13C solenoid confi guration allows reasonably straightforward scaling of the sample volume even at high frequencies. For samples that are inherently dilute (i.e. membrane proteins in lipid vesicles or proteins adsorbed on to solid substrates), it is often preferable to use l arger sample volumes. This is because sensitivity per unit volume scales as ~(1/d ) with respect to the rotor diameter while full rotor sensitivity scales as d2, so a larger sample diameter presents significant advantages for concentration-limited samples if sufficient RF strength and homogeneity can be achieved, Figure 2 3 [2]. In this chapter I present the design and characterization of a ssNMR magic angle spinning (MAS) pro be that utilizes a 1H LGR placed orthogonally to a 13C solenoid implemented on an NMR system with a 17.6 T magnet (750 MHz 1H frequency). The design was optimized for intrinsically dilute samples by utilizing a 4 mm rotor. The use of two separate coils all owed us to significantly increase both the length and number of turns in the solenoidal coil, making highly homogeneous B1 fields achievable even with the increased volume of the coil. 750 MHz Probe Assembly Sample Coil Assembly and Integration into a MAS Stator The probe design described and characterized in this chapter is an adaptation of a previously reported static low -E probe [18] The coil assembly consists of two RF coils which are orthogonal to each other. The outer coil is a rectangular LGR tuned for the 1H circuit and the inner coil is a solenoidal coil for the low gamma nucleus. In previous work this assembly was optimized fo r PISEMA experiments on static, oriented membrane -embedded protein samples.

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36 For the present MAS application, the coil assembly, Figure 2 4, was modified so that it could be integrated into a 4 mm MAS stator (model AMP4023001, Revolution NMR, Inc., Fort Co llins, CO) with a top spinning speed of 18 kHz. In MAS implementation of low E coils, the sensitivity of the detection channel benefits from a stator design where MAS bearings are placed further apart as this provides space for additional turns in the obse rve solenoid. The coil cavity available in the stator measures 11 x 12 mm in cross -section and 20 mm in length, which is substantially longer than the 12.7 mm length of our coil assembly. This stator is compatible with standard Varian 4.0 mm Pencil style r otors (Revolution NMR p/n AMP4088 001 or Varian p/n MSPA003006). The exact physical dimensions for both coils are provided in Figure 2 4. Regulation of sample temperature is accomplished by VT gas delivered through the side of the stator. The loop gap res onator was fabricated by forming a 0.25 mm thick, 9.0 mm wide copper strip around a 12.2 x 8 mm rectangular block. The ends of the strip were terminated with nonmagnetic chip capacitors (100B series, American Technical Ceramics) to complete the LGR. The resonator was attached to the 1H matching network using low inductance leads threaded through a Teflon platform that centers the coil assembly in the stator housing, Figure 2 6(a, b). The inner, low gamma coil is an 8 turn 4.6 mm ID x 8.3 mm long cylindrica l solenoid. The solenoid was made from 0.6 mm round copper wire (American Wire Gauge #22). Locating the low frequency coil closest to the sample maximizes sensitivity for direct detection. The homogeneity of the B1 field was improved by using variable spac ing between the coil windings. The solenoid leads were also threaded through the Teflon platform which centers the coil with respect to the LGR and the MAS stator.

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37 RF Matching Network The double tuned X 1H matching network implemented in our MAS probe is shown schematically in Figure 2 5. The design and performance of this RF circuit has been thoroughly described [18] For the purposes of the applications described here, the detection channel was tuned to 13C. It can be re tuned to any other low gamma nuclei by exchanging capacitors C7A and C8. Variable capacitors C5, C6, and C7 in the low frequency circuit are 1 to 10 pF trimmers (NMNT10 6E, Voltronics Corp., Denville, NJ). In the proton channel, C1 is a 1 to 6 pF trimmer (Voltronics NMQM6G), C2 and C3 are 0.3 to 3 pF trimmers (RP -VC3 6, Polyflon Co. Norwalk, CT). Non -magnetic fixed capacitors employed in the proton channel are Voltronics 11 series chips. In the low frequency channel, we used non -magnetic 100C series chips from American Technical Ceramics, Huntington Station, NY. The chip capacitor values for the proton LGR (L0 C0) had to be chosen to resonate it slightly above the Larmor frequency. This self resonance frequency is affected by the dielectric material of the stator and the coil platform, which are in close proximity. A small loop was inserted through a hole in the stator to pickup the resonant frequency, f0, of the entire stator assembly. Chip values (C0) were c hosen to place f0 between 780 and 790 MHz. Probe Body Construction The probe body was machined and assembled at the NHMFL. The outer structure is made of anodized aluminum. The upper plug at the top of the body tube is brass, Figure 2 6c. The RF platform i s copper, Figure 2 6f, and the top stator platform is PEEK (Polyetheretherketone). The end caps of the main aluminum body tube caused problems during assembly because they were machined with very close tolerances. Assembly requires putting them in and taki ng them out several times. They began galling during the assembly process from this putting in and taking out. If only one is stuck, a dowel of suitable material (Teflon was handy) and diameter can be

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38 used as a hammer to knock the plug out from the inside. With both stuck, the challenge is much greater. Subsequent probes have greater clearance planned on these parts. The copper parts are soaked in sodium bisulfate, washed with soap and water, and then quickly dried to remove any oils or oxidation. Gloves ar e worn during assembly to reduce reintroduction of contaminants and oxidizers. VT dewars were custom made by James Finley at GlassWorks (www.glassworks.com). Heaters were bought from Bruker for ease of interoperability and durability. Their heaters are be tter quality than others. Thermocouples are of type T (copper -constantan) from Omega Engineering, Inc. (www.omega.com). They come with a standard 2 prong thermocouple plug with the thermocouple installed in a stainless steel housing. The plug and housing a re removed to reduce the space required for the thermocouple. A jack for Bruker style probe thermocouples is installed to maintain interoperability with the Bruker spectrometer where this probe is installed. Tuning rods are fiberglass rods. The upper ends are turned down to accept a brass screwdriver type head that fits into the bottom of the variable capacitors. This screwdriver head and the knob at the base are glued to the fiberglass rod using 5 -minute epoxy, Figure 26(d, e). A label maker is used to make labels for the knobs. After applying the labels, a loop of shrink-wrap is put around the label to keep it in place. The 1H channel knobs are aluminum and the 13C channel knobs are brass colored. The tuning knobs are larger than the match knobs. This ap proach makes differentiating which knob does what much easier during normal use. This probe was the first to use a very narrow diameter, high pressure tubing for the MAS bearing and drive gases, Figure 2 6g. This tubing greatly reduces the space required for transporting air to the probe head. The unfortunate side effect of the narrow tubing is that higher pressures are required to get sufficient flow for higher MAS rates.

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39 Brass tubing (~1/8 diameter) was used as guides for the thermocouple and body/elect ronics air between the bottom and top of the probe. The VT air dewar had a stainless steel guide between the top and bottom of the probe. Tape is added to the outside of the dewar prior to installation to prevent it from rattling in the guide. The spring m echanism which holds the heater into the dewar also holds the dewar into the probe. The RF signals are transported from the base to the RF section via semi rigid coax cables, Figure 2 6g. The 1H channel has an N -type connector and the X channel has a BNC type connector to prevent accidental attachment of the wrong RF cable to either channel. The final probe head is shown in Figure 2 7 Testing and Specifications Power Efficiency and Homogeneity of RF Fields The low -E resonator MAS probe was fully characteri zed via NMR experiments using a 750 MHz Bruker AV2 system with an 89 mm bore magnet and a CPC MRI Plus model 19T300 1H amplifier. The power going into the probe was measured using a directional coupler and an RF power meter (Agilent E4416A meter with an E9 323A power sensor). Adamantane (Acros Organics) was used for direct observation of the 13C and 1H resonances for B1 field and homogeneity measurements since it is a low loss material and its dipolar couplings are inherently small due to molecular motion an d can be removed to first order by MAS at moderate rates. It was also used for calibrating chemical shifts and lineshape measurements. For restricted volume measurements, Kel -F spacers were used to reduce the sample length and to center the sample within the coils. 1H and 13C nutation experiments utilized a single, variable length pulse on the observe channel and, for 13C experiments, CW proton decoupling (83 kHz) was applied during acquisition. 13C homogeneity was determined by irradiating and monitoring t he carbon resonance

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40 at 38.48 ppm; 1H homogeneity was determined by irradiating and monitoring the unresolved proton resonances at an average position of 2.6 ppm. The maximum 1H power available on the spectrometer is 220 Watts, which is below the power li mit of the probe. With our limited available power, the maximum 1H decoupling field is achieved by bypassing the duplexer and connecting the amplifier output directly to the probe; this is the setup we typically use in ssNMR experiments. To measure maximum 1H nutation rates achievable by this setup using NMR, we prepared a sample of chloroform sealed in a 1 mm capillary with 5 -minute epoxy. The capillary was inserted inside a thick -walled rotor along with ground KBr to stabilize the spinning at ~1 kHz. The 1H nutation rate was then measured via indirect detection [22] B1 homogeneity measurements as a function of adamantane sample length are shown in Figure 2 8. Homogeneity is reported as the ratio of the signal intensities after 810 and 90 pulses (810/90). RF field strengths ( 1 kHz at 220 W of input power for 1H (resonant frequency of 750.2 MHz) and 72 kHz at 75 W of input power for 13C (resonant frequency of 118.6 MHz). As expected, the LGR coil for the proton channel, the increased number of turns in the solenoidal coil, and restricting the sample length to within the coils led to enhanced B1 homogeneity at both low and high frequencies. Example nutation profiles for both 1H and 13C can be seen in Figure 2 9. The length of sample in Figure 2 9 is 81% of the length of the solenoid. Isolation between probe channels was measured using a HP8752C Vector Network Analyzer (Hewlett Packard). Without external filters, the isolation achieved between the 13C and 1H ports is 45 dB at the 1H frequency and 24 dB at the 13C frequency. Placement of the 1H loop gap resonator as the outer coil leads in principle to less efficient performance on the high frequency channel, b ut this compromise is offset by orienting the

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41 resonator orthogonal to B0 and by the high RF homogeneity of the LGR. By choosing this geometry, the 1H B1 field in the x -y plane is not attenuated by rotation of the coil assembly from a static orientation orthogonal to the external magnetic field to an orientation in which the solenoidal coil axis is at the magic angle. More importantly, the placement of the solenoidal coil inside the assembly improves the filling factor on the observe channel. This helps to offset the loss of B1 field in the solenoid due to its magic angle orientation. Because the length of the solenoid is not limited by 1H wavelength effects, we are able to utilize an 8 turn solenoid, which further improves the performance of the 13C channel relative to multiply -tuned solenoids containing fewer turns. Power Handling and Stability The probes power handling capabilities were bench tested to determine if long, high power pulses led to either arcing or detuning of the resonant circuits. No arcing was observed during 80 ms long pulses in the 1H channel at powers exceeding 280 W, which corresponds to (1 kHz. However, the first implementation of the probe exhibited detuning of the 1H resonance by as much as 0.9 MHz once the decoupling pul se length exceeded 20 ms. The chip capacitors in the 1H LGR are heated up by the high current needed to produce strong decoupling fields, and this can lead to small changes in capacitor values. This problem was narrowed down to a lack of cooling mechanism for these chips. To correct it, a channel was cut in the Teflon platform underneath the chip capacitors, allowing the gases circulating inside the sample compartment to flow around the chips and cool them on all four sides. This measure significantly decreased detuning of the 1H channel to a much smaller, comfortable level, which does not require tuning adjustments during NMR experiments. A subsequent test has shown that high power detuning in the 1H channel can be eliminated if the 100B series chip capacit ors in the

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42 LGR are replaced by their temperature-compensated NP0 counterparts, such as non-magnetic version of 700B series. The 13C channel was stable under high power conditions with pulses up to 20 ms in length at powers exceeding 75 W ( 1 kHz) a nd 5 ms long pulses at 117 W (1 kHz). One of the first versions of the coil assembly did arc at lower power levels. The arcing took out a 1H HPPR/2 preamplifier slice at AMRIS. The probe was transported back to the NHMFL in Tallahassee for further testing and repair. This provided some good pictures of what arcing looks like, Figure 2 10. Hard arcing like we were experiencing makes an audible click too. Arc testing was done in a lab with an older high power amplifier. The power levels were slowly i ncreased and then once a satisfactory power level achieved, left to run for a few hours to make sure that no weaknesses were found from usage. This process resulted in a slight redesign of the 1H LGR. Originally the design called for two sets of two series capacitors in parallel. The final design uses two sets of three series capacitors in parallel. This reduces the voltage across each capacitor such that arcing is much less likely. Experience has shown that we are operating at the maximum power on the 13C channel before arcing at around 75 W. The 13C solenoid is not arcing to the LGR since when arcing occurs, there is no corresponding spike showing on the 1H reflected power. The next version of the probe this should be examined more carefully and verified so that the full 100 W available on the spectrometer can be used. However, even with this limitation on power, the efficiency of the 13C channel is high enough for our purposes due to the 8 turns in the solenoid. Shimming The probe shims adequately without spending extensive time. The 13C full width at half height for adamantane is 9 Hz at a sample length of 3.7 mm; the 0.55% linewidth is 83 Hz. For

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43 the full rotor length, 11.7 mm, the half height linewidth is 11 Hz. A small foot is observed in the 13C signa l which is similar to inhomogeneous broadening we have observed in a commercial XC4 probe from Doty Scientific. Our lineshape would likely be improved by using zero susceptibility wire in the solenoid which is closest to the sample, but the opportunity to test this hypothesis has not arisen. Another source of inhomogeneity may be the capacitors for the 1H coil. However, they are more physically distant from the sample, so we expect their contribution to the observed broadening to be less, relative to the 13C coil wire. RF -Induced Heating To characterize RF performance with typical biological samples, test samples containing either D2O or 0.15 M NaCl in D2O were prepared. Experiments were performed using the full rotor volume as well as more restricted sampl e lengths. Rotors were sealed with PTFE tape gaskets and sample lengths were varied using Kel F spacers. To measure RF -induced heating, aqueous samples described above were doped with 20 mM thulium 1,4,7,10tetraazacyclododecane 1,4,7,10tetrakis(methylen e phos -phonate) (TmDOTP5-) (Macrocyclics) as the temperature dependencies of the exchangeable proton chemical shifts in TmDOTP5are sensitive, linear, and well documented [23] In particular, the H(6) proton provides a nicely resolved resonance for monitoring temperature changes. Because of its high ionic strength, the relatively small concentration of TmDOTP5 is expected to contribute noticeable RF loss. The sample rotation rate w as regulated at 2 kHz, and bearing and drive air were supplied at room temperature. The sample temperature was regulated by means of an air stream cooled by a Bruker BCU 05 refrigeration unit and controlled by a BVT 3300. The RF heating experiment was run as follows: a presaturation pulse was applied to the probe for 40 ms at the test power level; this was followed by 5 ms of signal recovery before a standard pulse and acquire sequence. The duty cycle was maintained at a constant 3.8% while the

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44 presaturatio n power was varied. Before signal averaging, 256 dummy scans were run (taking ~5 minutes) in order for the sample to reach a steady state temperature. Example spectra are shown in Figure 2 11. The sample temperature rise due to RF irradiation can be seen in Figure 2 12. Even for the full rotor with 150 mM NaCl added to the TmDOTP5-, the sample temperature increased less than 15 K. For the 20 mM TmDOTP5samples, the heating was 7.3 K for a full -length sample (11.7 mm) at 168 kHz2, 6.5 K for a 6.7 mm length sample at 257 kHz2, and only 5.3 K for a 3.7 mm length sample at 280 kHz2. From Figure 2 12 we can see that the 150 mM added NaCl roughly doubles the amount of RF heating in the sample. The longer samples, which extend closer to the ends of the LGR coil w here the E field is known to be higher [24], reached a somewhat higher temperature than the 3.7 mm samples. Further samples incorporating lipids (50 wt %) were also tested (data not show n), with results similar to those seen for samples without salt. The relatively low RF heating observed even with higher salt conditions demonstrates that the LGR reduces the conservative E field within the sample to an acceptable level that will neither damage the sample nor significantly affect NMR measurements. This is particularly critical for high field spectroscopy since the conservative E field scales linearly with B0 for a fixed coil inductance and B1 field [18] The voltage across a coil, which determines the conservative E field, is proportional to the impedance of the coil, 0L, where 0 is the Larmor frequency. The use of low inductance LGR for generation of 1H RF fields had been shown to reduce RF heating in the sample by an order of magnitude during decoupling [18] At the same time, our detection solenoid has multiple turns with i nductance much higher than that of LGR. The strength of its conservative E field is mitigated by 4 times smaller Larmor frequency of 13C.

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45 Also, the amount of time the 13C channel is transmitting is typically less than half the time the 1H channel is transm itting, since the 13C channel is only transmitting during the excitation part of the experiment while 1H decoupling is used during both excitation and acquisition. To be safe, it is prudent to compare amounts of heat generated in the sample by each of the coils. A simple way to estimate heating contributions from each RF channel under normal operating conditions is to use changes in a probes Q or 90 pulse length when switching between lossy and non-lossy samples [9,18] For the Q measurement, the amount of RF power dissipating in the dielectrically lossy sample for each kHz2 of RF field is shown in Equation 21 in units of W/kHz2 where QBIO i s the Q of a probe loaded with lossy (biological) sample and QNL and NL are the Q and power efficiency of a probe with a nonlossy reference. NL BIO NL heatQ Q q1 1 (2 1) For our measurements, we used 150 mM NaCl aqueous solution as a lossy sample. We chose water to serve as a nonlossy reference in order to maintain a similar dielectric constant and minimize retuning of the probe between the measurements of Qs. Both samples occupied full volume of the rotor (11.7 mm in length). The Q values and calcul ated heat dissipation rates, qheat, are listed in Table 2 1 for both 1H and 13C channels. To compare amounts of 13C and 1H heating induced in the sample under typical operating conditions, we estimate heating during an actual DQDRAWS experiment, an experim ent used extensively in Dr. Longs lab. If the 1H 93 kHz decoupling field is applied for 40 ms every second, the resulting heat dissipation is 1.02x(103)x932x0.04 = 0.35 Joules into the sample per transient from the 1H channel. The CP pulse and windowless excitation pulse train on the 13C channel last half as long (20 ms) with RF fields held at 42.5 kHz, resulting in 4.67x42.52x0.02 = 0.17 Joules of heat dissipated in to the sample. Thus, with the current probe design, the 13C and

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46 1H channels contribute le vels of heating on the same order of magnitude in the sample under normal operation. Frictional Heating The aqueous samples used for measurement of RF heating will not spin reliably at high sample rotation rates, so powdered lead nitrate (Pb(NO3)2) sample s were used to measure frictional heating due to sample rotation. The temperature dependence of the 207Pb chemical shift (156.4 MHz at 17.6 T) is also well documented [25] To reduce the density of the MAS sample to levels relevant to biological samples, lead nitrate was mixed with NaCl. Fine, ground crystals of NaCl were mechanically mixed with fine, ground crystals of lead nitrate to achieve a mixture that was ~10% lead nitrate by weight and to achieve a biologically relevant density of ~2.4 g/cm3. Spectra were collected using a standard pulse acquire sequence at different sample rotation rates while holding the VT air temperature constant, Figure 2 13. A temperature equilibrium time of at least 10 minutes was used at each spinning speed. The full 57 mL sample volume of a thick walled rotor was used for these measurements. As shown in Figure 214, frictional sample heating was a maximum of 20 K when spinning at 13 kHz with a VT temperatur e of 298 K. It was noted that different bearing and drive pressures resulting in the same sample rotation rate cause varying levels of frictional heating. Sensitivity Measurements Measurements of sensitivity were performed using crystalline, natural abundance glycine ( -form) to allow comparison to other published work. The veracity of this standard for determining true S/N is limited given that the quality of the spectra are determined by a number of interrelated factors. Measurements were done for the fu ll sample length (11.9 mm) in a thin walled rotor (95.6 mL sample volume) with a sample mass of 115.4 mg spinning at 13 kHz. Sample lengths of 8.4 mm with 83.6 mg of sample, 6.9 mm with 70.1 mg of sample, and 3.9 mm

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47 with 38.3 mg of sample were also examine d. All spectra were collected at 13 kHz MAS. Signal was measured with ramped cross polarization sequence and 94 kHz SPINAL64 decoupling [26] during acquisition. A recycle delay of 30 sec onds was used and signal was averaged over 1, 2, 4, and 8 scans with 2 dummy scans. Data (4096 points with a dwell of 10 ms) were Fourier transformed (without line broadening), phased, and maximum signal was measured between 40 50 ppm for comparison to noi se between 70 and 90 ppm, Figure 2 15. There are several formulae for calculating S/N. We have chosen a standard definition of S/N as being PH/(2*NRMS), where PH is signal peak height and NRMS is the root -mean -square noise amplitude. The sensitivity of t he probe was also characterized for a variety of sample lengths in order to allow quantitative determination of optimal conditions for applications in which one may be examining mass -limited samples or concentration -limited samples with either simple pulse sequences or pulse sequences requiring high B1 and high homogeneity on the 13C and/or 1H channels for the best possible performance. For these measurements, the S/N is normalized to the square root of the number of scans, allowing S/N comparisons independent of the number of scans, as well as to the weight of the individual samples. As can be seen in Figure 2 16, the best S/N per mg is with the smallest sample length and remains high for sample lengths less than 6.9 mm (83% of the coil length). The best overall S/N is achieved for samples lengths on the order of 6.9 mm and longer. The signal quality does not increase greatly once the sample length is on the order of or greater than the coil length (8.3 mm) and resolution is compromised for the longer sample s. For most applications that are concentration limited rather than mass limited, a sample geometry in which the rotor wall is the minimum thickness possible for a given spinning speed is optimal. A sample length on the order of 7 mm provides optimal S/N with acceptable RF

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48 homogeneity. Increasing the length of the sample beyond this point yields little in improving S/N and can even be detrimental to making quantitative measurements using standard ssNMR pulse sequences due to incomplete excitation of the fu ll sample. For samples with limited quantities, the length of the sample can easily be adjusted using spacers allowing optimal S/N and RF performance. Cross Polarization Measurements For static cross -polarization (CP), the best magnetization transfer is a t the Hartmann Hahn matching condition, which means that both nuclei are nutating at similar rates during the spin lock [27] When optimizing CP on a MAS sample, the best transfer conditions are when the nutation rates differ by +/ 1 or 2 times the MAS rate [28,29] A CP profile can be generated by holding the RF field constant for one resonant freque ncy and varying the RF field for the other resonant frequency through these matching conditions. The symmetry and widths of the peak matching conditions as well as the overall profile reveal how homogeneous the B1 fields are at the two frequencies and how well they overlap with respect to the sample [5]. CP matching profiles using square spin lock pulses were collected by fixing the 1H power at ( 1 kHz and varying the 13C power, Figure 2 17. Measurements were performed at a sample rotation rate of 10 kHz on adamantane samples that were 3.7 and 11.7 mm in length. The symmetry of the peaks indicates that the homogeneity and the overlap of the B1 fields are quite good. For the longer samples the matching conditions become broader and less symmetric but are still considerably better than multiply resonant coils, particularly those that are not properly balanced [5]. This emphasizes the importance of homogeneity for efficient cross polarization. The similarity of the measured profiles to an ideal profile is striking given that the two B1 fields are generated by two orthogonal coils with different geometries.

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49 Performance with a Biologically Relevant Sample To illustrate the performance of the Low -E MAS probe we collected a standard CP MAS spectrum on a microcrystalline protein. Lysozyme crystals were made by dissolvin g lysozyme at a concentration of ~50 mg/mL in deionized water. To this solution an equal volume of precipitation solution containing 3 M NaCl in 50 mM Tris buffer, pH 7.0 was added. The 1:1 mixture of protein solution and precipitation solution was left to evaporate at 40 C for 2 days leading to crystal formation. The crystals were then collected by centrifugation and loaded into a rotor. A CPMAS spectrum, Figure 2 18, verifies the crystallinity of the sample. Performance Using Multipulse Windowless RF Se quences DQDRAWS (Double Quantum Dipolar Recoupling in A Windowless Sequence) experiments [30] were performed on a tripeptide, *G*AV, which is 13C enriched on the first two amino acids ( the enriched peptide is diluted to 10% with natural abundance peptide and crystallized). These experiments are useful at intermediate rotation rates (5 -8 kHz) for determining torsion angles in peptides [31] yet, like many recoupling sequences, their performance is dependent on the availability of strong, homogeneous B1 fields [32] For these experiments, the CP contac t time was 2.2 ms, cw decoupling was applied during the mixing period and SPINAL64 decoupling [20] was applied during acquisition. The MAS rate was 5 kHz, which corresponds to a /2 pulse of 5.88 ms for the rotor -synchronized DRAWS sequence. Even with a full rotor (sample length 11.7 mm) and 5 kHz rotation rate (~104 kHz 1H field and 42.5 KHz 13C field) a DQ excitation efficiency of >25% was achieved for the enriched spins, which have a dipolar coupling of ~250 Hz. A 2D DQ CSA spectrum was collected with a t1 increment of 20 s and evolution of 5.12 ms with 48 scans per slice and demonstrates the improved resolution of these experiments with high magnetic field, Figure 219.

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50 DQDRAWS data were also collected on a peptide in a lipid environment to demonstrate the utility of the low -E probe in examining protein structures under conditions in which the protein is inherently dilute. The sample consists of a 21 amino acid peptide ( KL4) isotopically enriched at two adjacent 13C positions and reconstituted in a lipid environment at a lipid:peptide molar ratio of >50:1. The sample was packed into a 6.7 mm length as this gave a reasonable filling factor for the amount of sample availab le. The DQ -filtered spectrum of this sample, Figure 2 20, demonstrates the advantages of using a selection filter to simplify complicated spectra. The 2D DQ -CSA data validate the ability of this technique at high fields to isolate and characterize differen t peptide conformations if suitable RF fields are available without compromising the integrity of the sample. Figure 2 20 also shows the improvements that can be had in fitting CSA -CSA correlation data by moving to a higher B0 irrespective of the probes us ed due to the increased spans of the CSAs.

52 Figure 2 1. Spectra of ~2530 mg of *G*GV peptide spinning at 5 kHz MAS at 500 MHz and 750 MHz. The green spectrum is taken at 500 MHz (11.7 T) and the blue spectrum at 750 MHz (17.6 T). The 750 MHz spectrum covers a wider set of frequencies (compare peak patterns) and has finer detail as shown in the subplot of +/ 500 Hz from the carbonyl resonance. The two carbonyl peaks cannot be distinguished at all at 500 MHz, but begin to separate at 750 MHz. They are even more distingui shable at 900 MHz. Also, the S/N of the two experiments is quite similar, as evidenced by the noise levels in the baselines, even though the spectrum at 750 MHz took 1/4 the time to acquire (64 scans vs 256 scans). The increase in CSA can be seen in the sp inning sidebands of the 750 MHz data extending further out at higher magnitudes. The spinning sidebands are spaced at 5 kHz in both the 500 MHz and 750 MHz data.

54 Figure 2 3. Relative sensitivity as a function of rotor diameter. The relative sensitivity of ssNMR as a function of rotor diameter increases as d2 when looking at full rotor signal sensitivity, where d is the diameter of the rotor. It decreases as 1/ d when sensitivity is measured per unit volume. The following assumptions were used in calculating this figure: 1) the solenoid coil diameter is 0.6 mm greater that the rotor diameter, 2) the length of each coil is twice its diameter, 3) a low -E type circuit is used on the 1H channel to minimize wavelen gth effects, 4) the rotor has a wall 0.4 mm thick, 5) B1 homogeneity remains constant for each rotor diameter since the coil length to diameter ratio remains constant, 6) the sample is constrained to 0.8 times the length of the coil. This figure shows that for mass limited samples, the smaller the rotor diameter the better, but for concentration limited samples, larger diameters are better. The sweet spot for both considerations is around a 4 mm diameter rotor.

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55 Figure 2 4. The dimensions of the coil asse mbly are in millimeters. The leads of the 13C solenoid coil press fit into the Teflon platform, holding it suspended inside the 1H LGR.

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56 Figure 2 5. The probe schematic. The schematic shows the separate circuits for the 1H and 13C matching networks. Is olation is achieved through the orthogonal placement of the coils. L0 C0 forms the 1H loop gap resonator with the detection solenoid inside (L1). Inductors L3 and L4 (5 10 nH each) represent flexible leads connecting sample coils to the 1H and 13C circuits. C1, C2, and C3 are variable capacitors for, respectively, matching, balancing, and tuning the 1H LGR. In the low-frequency channel, C5 is used for matching while C6 and C7 tuning capacitors are connected to a single tuning rod via a gear mechanis m. Retuning to different observe nuclei (e.g. 15N) is done by replacing a tuning chip, C8, and a balancing chip, C7A. A low -voltage 1H rejection trap, L2 C4, is placed at the entry of the 13C RF cable.

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57 Figure 2 6. Pictures from assembling the probe. A) The coil assembly before inserting into the stator has the flexible leads attached and the external capacitors on the leads. B) After the coil assembly is inserted into the bottom of the stator the 13C lea d (wires) and the 1H leads (plates on either side of the brown block in the middle of the Teflon) are visible. The brown (PEEK) block has a hole in it for cooling the LGR capacitors. C) The top plate for the body tube has guide and attachment holes. The holes that have tuning rods going through them have plastic lining to prevent wear. D) The handle ends of the tuning rods have different knobs depending on their use and are individually labeled. E) The tuning end of the tuning rods have metal screwdriver type ends epoxied on. The rod without a metal end will have a gear attached for turning the two 13C tuning capacitors. F) The tuning capacitors are mounted on a copper plate. G) The RF lines are carefully bent around a hard object to line the connectors up with holes on the pr obe base. Note the small diameter air lines coming out as well. A B C D E

60 Figure 2 8. Homogeneity plot for both channels. The B1 homogeneity characteristics for the 1H (blue squares) and 13C (red circles) channels as a function of sample length is high and improves when the sample is confined within the coil, as expected. The 13C solenoidal coil length, 8.3 mm, is indicated by the green, dashed, vertical line.

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61 Figure 2 9. Nutation profil es for both channels. Example nutation profiles for the 1H (blue) and 13C (red) channels collected using a 6.7 mm long adamantane sample show that the homogeneity is very good on both channels even for this sample length. Each peak corresponds to the monit ored resonance as a function of the pulse length in 0.5 s increments. The 13C profile used 3 s recycle delays, which is a little short for adamantane. This is why the peaks of the profile are biased rather than perfectly sinusoidal.

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62 Figure 2 10. Probe arcing. During initial testing of the probe it arced seriously. This is a picture of what a probe is not supposed to do. The arc was across one of the capacitors in the 1H LGR circuit. The arcing scorched the Teflon platform. The scorched parts of the plat form had to be removed to prevent rearcing in those spots.

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63 Figure 2 11. Example TmDOTP peaks with increasing RF input. An example TmDOTP H(6) heating run shows the peaks shift toward 0 ppm as the temperature increases. The temperature spread also incre ases as indicated by the increasing peak width. The temperature spread is a result of the cooling effects of the VT and MAS competing with the RF heating. The no heating peak is used as a reference point and the temperature of the sample is estimated using a slope from that point of 0.87 ppm/K from Zuo et al [23]

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64 Figure 2 12. RF heating. The average RF sample heating at three different sample lengths and two salt concentr ations are shown. Red filled circles are 20 mM TmDOTP5 with a 3.7 mm sample length. Red filled squares are 20 mM TmDOTP5and 150 mM NaCl with a 3.7 mm sample length. Blue filled symbols correspond to the same solutions with a 6.7 mm sample length, and th e empty, green, symbols correspond to the same solutions with an mm sample length. Lines are linear fits to the data as a visual guide. Note that because of its high ionic strength, small concentrations of TmDOTP5still contribute significantly to RF loss. The RF heating remains under 15 K for all samples and either decreasing the sample length or the salt concentration further reduces the heating. Average power was varied by keeping the duty cycle constant at 3.8% power. A delay of 5 ms between the were run before acquiring to make sure the sample had reached equilibrium

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65 Figure 2 13. MAS heating spectra. These 207Pb s pectra are used to create the MAS heating curve shown in Figure 2 14. The peaks picked for the data are indicated by the triangles. The temperature gradient across the sample increases as MAS rate increases. Note that the left peak gets taller than the rig ht peak above 11 kHz. The temperature is equal to 1.32*(peak location + 3714) [33]

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66 Figure 2 14. MAS heating. The frictional heating due to MAS reaches 20 K for speeds of 13 kHz, which is enough to be a problem for biological samples, but it can be mitigated by cooling the rotor with chilled VT gas. The sample temperature was monitored using a sample containing 10% lead nitrate (Pb(NO3)2) diluted with NaCl to reduce its density. Th e gas lines were kept at room temperature. The line is a quadratic fit through the origin. The initial temperature drop is due to Joule -Thomson cooling.

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67 Figure 2 15. Glycine spectrum for measuring S/N. This is a NAGLY 13C CPMAS spectrum after 8 scans with a sample length of 6.9 mm containing 67.3 mg of glycine spinning at 13 kHz. Inset is a magnification of the noise used in the S/N measurement. This particular spectrum has a S/N measurement of 301.

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68 Figure 2 16. Signal -to -noise for various sample le ngths. This shows S/N for NAGLY as a function of sample length. Shown are the S/N normalized for the number of scans (solid blue circles, left axis) as well as the S/N per unit mass (open red squares, right axis), also normalized for the number of scans.

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69 Figure 2 17. CPMAS matching condition profile for adamantane at 10 kHz MAS using a square spinlock pulse on both RF channels. The 1H RF field was held constant at ( 1/2 ) = 35 kHz while the 13C B1 field was varied; the signal is graphed as a function of the RF mismatch. The solid blue line corresponds to a sample length of 3.7 mm; the dashed red line corresponds to a sample length of 11.7 mm. The X axis is the average 13C B1 field minus the average 1H B1 field. The longer sample (11.7 mm, dotted line) has broader, weaker matching conditions. This is from the wider range of RF energy the sample is exposed to due to the lower homogeneity of the 13C B1 field. The shorter sample (3.7 mm, solid line) shows excellent agreement with theory with maximal signal at mismatch levels equal to integer values of the spinning speed.

72 Figure 2 20. An example showing the improvements in signal quality in going to higher field. A) CPMAS and DQ -filtered spectra for the 21 amino acid peptide KL4 13C -enriched at positions L9 and L10 and incorporated into DPPC:POPG lipid vesicles at a peptide:lipid molar ratio > 1:50; the signals in the aliphatic region are primarily from the surrounding lipids. B) 2D DQ CSA correlation data for the KL4 sample alo ng with best fit simulations. Closed and open symbols are data collected at 750 and 500 MHz, respectively; lines correspond to the signal trajectories for the best fit ( ) simulations at the two fields. C) 2 evaluation of simulations with varying whil e holding at a value obtained from DQ buildup experiments; solid and dashed lines correspond to fitting of data at 750 and 500 MHz, respectively. Note the improved selectivity of the 2 evaluation at 750 MHz due to the increased CSAs at the higher magnet ic field. C h e m i ca l S h i f t ( p p m ) A 0 5 0 1 0 0 1 5 0 2 0 B

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73 Figure 2 20. Continued Relative 2 Relative 2 C

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74 CHAPTER 3 RF EXCITATION PROFIL ES BACKGROUND AND PR IOR ART FOR OPTIMIZA TION Introduction One method of optimizing NMR experiments is by improving the hardware used to run the experiments. NMR experiments can also be improved by optimizing the way NMR experiments run. An NMR experiment consists of transmitting RF energy into a sample and then d etecting the resultant RF signal the sample emits. The RF signal transmitted into the sample can be as simple as a single pulse at a single amplitude, frequency, and phase, or it can be many hundreds of pulses each at a different amplitude, frequency, and phase. Experimental setups are never perfect. As discussed in Chapter 2, the RF fields are not perfectly homogeneous. Also, the static magnetic fields are not perfectly homogeneous. The RF pulses have finite lengths and are not perfect in phase, frequency or amplitude. Even in a homogeneous magnetic field the various nuclei in an experiment may be resonant across frequencies spanning many kHz due to the chemical shielding described in Chapter 1. In fact, these frequencies are often the information desired from the experiment. However, exciting all of the nuclei uniformly across wide bandwidths can be difficult. Ideally, one could transmit exactly on resonance for all the nuclei of interest and transmit nothing at the resonant frequencies of all other nuclei In practice this is not possible. Many experiments have been designed to measure the various properties of molecules; the goal of this research is to take some of these experiments and rebuild them to be more tolerant of the imperfections in the experime ntal process. In Chapter 2, hardware development addressed the problem inhomogeneity of the RF field around the sample. In this chapter I explore the effect of the frequency offsets due to chemical shifts.

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75 A thorough understanding of the relationship betw een RF pulses and frequency offsets set the stage for Chapter 4 in which compensated pulses are designed and optimized by using computational optimization to design pulse sequences more tolerant to frequency offsets. The goal of computational optimization is to find the sequence of RF energy that when transmitted into the sample, maximizes the signal of interest from the sample in the presence of various imperfections of the system. The RF energy has four main variables: length of time applied, magnitude, f requency, and phase. Typically, the RF energy is not constant in an experiment, but is pulsed, which means that each of these parameters can and may be varied throughout an experiment. However, there are practical limitations. The sample and the hardware determine the overall length of time the RF can be applied, the maximum magnitude used, and the speed with which the phases and amplitudes can be changed. Exceeding the maximum length of time or magnitude can cause probe arcing and/or sample degradation through heating. The RF frequencies used in an NMR experiment are determined by the nuclei of interest, their molecular environment, and the strength of magnet used. The base frequency for a nucleus of interest is determined by a (or magnetogyro) ratio char acteristic for that nucleus times the strength of the magnetic field. For 1H nuclei in a 17.6 T field, that frequency is 750 MHz; for 13C nuclei in a 17.6 T field, that frequency is 188.6 MHz. The molecular environment around each nucleus also affects its resonant frequency; at 17.6 T variations of up to 40 kHz are seen for 13C nuclei in biomolecules. The phase of the RF, then, is the only completely free variable. Therefore, the goal of computational optimization is to find the sequence of RF pulses, defi ned by their length, magnitude, frequency, and phase, for a given set of nuclear parameters to obtain the desired

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76 information about the nuclei using a NMR simulator. Once a suitable solution has been found, it is tested on a spectrometer to verify that it really works experimentally. Mathematical Representations of NMR Experiments To simulate an NMR experiment, one must have some understanding of the math behind NMR and how to accurately model an experiment using a simulator. Accurately modeling an experime nt via simulation requires understanding NMR experiments, usually learned at an NMR facility, and how to run a simulator, usually learned from the manuals published about them. This section gives a brief overview of the mathematics used to model NMR experi ments to aid in understanding both the simulations and possible approaches to optimization. A quantum mechanical property of atomic nuclei is spin angular momentum, specified by their spin number. Nuclei with nonzero spin numbers are said to have nuclear s pin and are NMR sensitive due to transitions between nuclear spin states. In the absence of a magnetic field, these states are equal in energy. When a magnetic field is applied, these spin states are no longer degenerate with an energy separation defined b y the Larmor frequency, which is equal to minus the gyromagnetic ratio of the nucleus times the magnitude of the magnetic field. Since this is a resonant frequency, the applied RF is usually as close to the Larmor frequency as possible. Describing what happens when RF is applied is easier if we switch from a laboratory frame of reference, to a frame of reference rotating at the frequency of the applied RF. If the applied RF is at the Larmor frequency (on resonance), its effects can be described by simple ro tations. In the presence of a magnetic field the average magnetic field generated by a population of nuclei with spin will be aligned with the magnetic field and is referred to as bulk magnetization, which by convention lies along the z axis at equilibriu m. There are two main ways to track the bulk magnetization of spin1/2 NMR active nuclei tumbling isotropically in a magnetic field using linear algebra. The first method uses the Pauli spin matrices as a basis set for a spin 1/2

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77 system. This method follow s the true quantum mechanical behavior of isolated spins most closely. The second method is to assume a population of nuclei with a net magnetization and to treat the bulk magnetization as a vector in 3D space and use vector rotation matrices to rotate the vector in 3D space in response to RF pulses and the resulting precession of the magnetization. In their simplest forms, both of these methods ignore relaxation and omit interactions added by the molecular environment of the nuclei. Pauli Method Spin 1/2 p articles have 2 available states, usually represented by the vectors [1 0]T and [0 1]T. Assuming a frame of reference in which the magnetic field is along Z, the Pauli matrices, Equations 3 1 through 3 3, are a convenient basis set for the superposition of states when operating on a spin 1/2 system. Ix 1 2 0 1 1 0 (3 1) Iy 1 2 0 i i 0 (3 2) Iz 1 2 1 0 0 1 (3 3) Each matrix can be thought of as representing the magnetization along one of the principle axes in 3D space. Bulk magnetizat ion with arbitrary direction and magnitude can represented by linear combinations of the Pauli matrices as shown in Equation 34 where xarb, yarb, and zarb are constants. Iarb xarbIx yarbIy zarbIz (3 4) Equation 3 4 can be thought of as the conversion from 3D Cartesian space to the 2x2 matrix quantum representation of the superposition of states. By convention, the static magnetic

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78 field is along the Zaxis. The RF is applied in the X Y plane and disturbs the system away from equilibrium. In the rotating frame, applying an RF field resonant to the energy splitting of a spin 1/2 particle rotates the bulk magnetization, initially at Iinit, through an angle, about the axis of the RF field, Irot as illustrated in Figure 3 1. The rate of this rotation is referred to as the nutation rate, The nutation rate is the frequency (usually specified as /2 Hz) that the magnetization returns to Iinit under continuous RF application. Nutation rate increases with applied RF power, so the stronger the field the higher the n utation rate. This leads to the confusing practice of referring to power levels in NMR by either RF power levels in the laboratory frame (in either watts or dB attenuation) or the nutation rate in the rotating frame. Nutation rate is the most standard meth od since it normalizes for any differences between NMR spectrometers and probes. The angle the bulk magnetization rotates through, is determined by the pulse length, measured in either units of time (usually s) or angle (degrees or radians), and the RF nutation rate. When the RF field is applied at exactly the resonant frequency of the nucleus of interest, i.e. on resonance, the bulk magnetization rotates around Irot through an angle of degrees. However, if the RF field is off resonance, the bulk magnetization will experience a stronger effective field causing it to rotate through an angle greater than around an axis rotated towards Iz from Irot. This is because the off resonance part o f the static magnetic field (B0 in the Z direction) contributes to the magnetic field experienced by the spin in the rotating frame. This is explained by observing in the rotating frame. If a spin is rotating at a frequency different than the rotating fram e is spinning at, it will appear to rotate along the Z axis at the difference between the rotating frames frequency and the spins frequency. The rotation around the Z axis can be modeled as an RF pulse around the Z axis. Thus, the two magnetic fields are at right angles and are combined through vector addition as illustrated in Figure 3 2. Thus, an RF signal applied

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79 from a spins resonance with a power of nut, rotates the spin with an effective magnetic field, eff, which is the magnitude of the vecto r sum of and nut, Equation 3 5. eff (nut)2 ( )2 (3 5) eff is the effective pulse length in degrees experienced by the spin, Equation 3 6. effeffnut (3 6) The axis that the pulse drives the magnetization around is given by the vector sum of nut and is always along the Z axis since the rotating frame rotates around the Z axis. The bulk magnetization rotation that the RF pulse causes can be expressed mathematically as a complex exponential. For example, Equation 3 7, an RF pu lse applied along the X axis, or Ix, results in a rotation of degrees around Ix. Rx() exp( iIx) (3 7) Equation 3 7 can be represented using a matrix by doing a Taylor expansion of the exponentiation, Equation 3 8, where E is the identity matrix. Rx() E cos2 i 2 Ixsin2 cos2 0 0cos2 0 i sin2 i sin2 0 cos2 i sin2 i sin2 cos2 (3 8) Mathematically, the final position of the magnetization, Iend, after a pulse can be calculated by front multiplying the initial magnetization, Iz, by Rx and rear multiplying it by Rx 1 as shown in Equation 3 9. Iend Rx() IzRx 1() (3 9) Due to the nature of Rx, Rx 1 is just the complex conjugate of Rx. Evaluating Equation 3 9 leads to Equation 3 10 for the final solution.

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80 Iend 12 cosi sin i sin cos (3 10) That solves the problem nicely for a rotation about Ix starting at Iz, but what is really needed is a more general solution for a rotation with an arbitrary starting point, rotation axis, and rotation angle. A general rotation about an axis, A is shown in Equation 3 11. RA() E cos2 2 i n I sin2 (3 11) nI can be expressed in terms of and the Pauli matrices, Equation 3 12 and Figure 3 3. n I Ixcossin Iysincos Izcos (3 12) A rotation from Iinit to Iend around axis A is implemented in Equation 3 13. Iend RA() IinitRA 1() (3 13) It is important when using Equati on 3 13 to remember to invert RA rather than just take the complex conjugate like we could do for Rx. Equations 3 11 and 3 13 allow for rotation about an arbitrary axis by an arbitrary angle and include off resonance effects. The result is a 2x2 matrix and it is often handy to convert this result into Cartesian ( x y z ) components for visualization. Equation 3 14 shows how to do this. ( x y z ) 2 real trace (RAIinitRA 1Ix), trace (RAIinitRA 1Iy), trace (RAIinitRA 1Iz) (3 14) For further enlightenment, the best reading is Cavanagh et al [34] but some other good references are [1,35 38] 3D Vector Method An alternate way of deriving the same information is to use the kinematic method of rotating vectors in 3 -space. The rotation matrix for rotating an initial magnetization vector, Iinit, about a unit vector K = [ kx ky kz]T by eff degrees, is given in Equation 3 15 [39]

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81 RK() kxkx ckxky kzskxkz kyskxky kzskyky ckykz kxskxkz kyskykz kxskzkz c (3 15) Equation 3 15 uses the abbreviations c = cos s= sin and = 1 cos Implementing RK( ) is shown in Equation 3 16 and illustrated in Figure 3 4. Iend RK() Iinit (3 16) This method gives the same results as the Pauli matrix method for isolated spin1/2 nuclei tumbling isotropically and is physically more intuitive. Off-Resonance and Non-I deal Rotations Offresonance effects in NMR are important for several reasons. The 13C spectrum of a peptide can span 300 ppm. Few of the carbon nuclei will be exactly on resonance for RF transmitted at a particular frequency, so it is important to use a p ulse sequence that evenly excites all the nuclei of interest. Off -resonance causes non -ideal rotations. Imperfect rotations can also a result from the inhomogeneity of the applied RF field. The RF pulse is not exactly the same strength throughout the sampl e, some spins experience different RF rotations than others. In longer, multipulse experiments, these imperfections accumulate, sometimes causing destructive interference and significantly reducing the desired signal. Solids Switching from running experime nts on liquid samples to solid samples significantly increases the complexity of simulating the experiment. Most of the work mentioned so far has been done assuming the NMR is performed on liquid samples. The molecules in a liquid tumble isotropically at a rate that is much faster than the timescale observable by NMR, including the RF pulses. This means that many of the interactions in a molecule are averaged out. The chemical shift anisotropy (CSA) and dipolar couplings in particular are averaged out. When the

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82 molecules no longer tumble isotropically, such as in liquid crystals or lipid membranes, these interactions are not completely averaged out. This is also true for samples that have even more restricted movements such as in polymers, glasses, or crystals. Without the averaging effect of molecular motion, the CSA and dipolar effects can significantly affect pulse sequences efficacy. One method of removing or averaging out the CSA and other interactions is to mechanically spin a sample rapidly at what i s termed the magic angle. This can average out most effects, but gives the operator control of how much gets averaged out. Also, through careful RF pulsing in synchrony with the rotor, selected interactions of interest can be refocused. Modifying the pr evious mathematical representations to model solid state NMR would require the addition of at least two main things: orientation dependence and time dependence. Since the molecules in a solid are no longer tumbling isotropically, the orientation of a sampl e inside the magnet matters. Doing single crystal NMR can show this well. Examples of what different crystal orientations might look like are shown in Figure 3 5. Crystallized solid samples are usually ground to fine powder which means that the NMR signal will be the sum of all crystal orientations, called a powder pattern, Figure 3 6. The time dependence is to model magic angle spinning. Magic angle spinning creates time dependence in the signal since each particle in the sample is at a different location throughout a revolution. Rather than reinventing the wheel and having to verify a new simulator for solids, I decided to use existing simulators that have been verified and accepted by the general NMR community. Simulators There are two ways to evaluate pulse sequences experimentally and using numerical simulations. The use of optimizing pulse sequences using experimental evaluation, Figure 3 7 [40] has s hown some success. This is the most reliable method of finding a pulse sequence that will actually achieve the signal you want. Unfortunately, it also has two major problems. First,

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83 spectrometers are expensive and experiments can take a long time to run, p articularly the more complex experiments. Most of the experimental time is from waiting for the sample to relax back to equilibrium after the last scan. For example, the inversion experiments discussed in Chapter 4 required a relaxation time of 7 seconds p er scan. Each data point required 16 scans and at least 41 data points were required for each experiment giving a total experiment time of an hour and 15 minutes. It can take hundreds to thousands of evaluations to converge to a solution. This means that l ots of spectrometer time has to be spent optimizing a particular pulse sequence before it can be used to find the molecular information we are seeking. The second problem is generalization. A pulse sequence optimized on one spectrometer will not necessaril y work as well on another spectrometer or even the same spectrometer with a different probe. The solutions are often over fit to match the peculiarities of a particular spectrometer setup. A faster, cheaper, and more general method of testing pulse sequenc es is to use a numerical simulation, Figure 3 8. An RF experiment that may take hours to run on a spectrometer can be run on a simulator in a fraction of a second with infinitely good S/N and no delays waiting for a sample to return to equilibrium. With a cluster of computers, very complex experiments can be run even faster or many experiments can be tried in parallel. Also, a simulation can be used to find a general solution that is not specific to any particular spectrometer or it can be used to optimize particular experiments for different spectrometers and probes with different RF characteristics. The one downside to using a simulator is that one has to be very careful that the setup between the simulator and the spectrometer eventually used to test the pulse sequence are as similar as possible and that the simulation accurately represents experimental limitations.

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84 There are three published simulators currently used widely in the NMR community: Gamma [41] SIMPSON [42] and SPINEVOLUTION [43] Independent labs also have developed a wide variety of simulation programs for their specific problems. Gamma is a set of C++ libraries for doing NMR simulations that has also been ported to the Python language. It is used by writing a program that describes the experiment, and then compiling and running that program. Gamma was originally written at ETH Zrich, but is now maintained at the National High Magnetic Field Laboratory in Tallahassee, FL. The routines have not been optimized for speed, so they are slow. The need to write, compile, and then run the pr ograms further slows and complicates methods when many, automatically generated simulations need to be run. Also, Gamma is no longer consistently maintained. Consequently, Gamma was not chosen as a simulator for this project. In 2000, Dr. Niels Nielsons l ab at the University of Aarhus published SIMPSON, a simulation program written primarily in C with input files written in TCL. Having the interface written in TCL makes it easier to work with than writing each simulation as its own executable. SIMPSON has bugs when using explicit phase cycling of RF pulses. Consequently, a filter command is often used. Phase cycling is a method of varying the overall transmitter and receiver phases to create destructive interference in the unwanted signals and constructive interference in the desired signal. The filter command just zeros out elements of the system density matrix rather than actually doing a phase cycle filter which oversimplifies the behavior of an NMR system. Dr. Robert Griffins lab published a simulator in 2006 called SPINEVOLUTION (referred to from here on as spinev). It is distributed as a compiled binary and uses a set of custom text files as input. Spinev has phase cycling explicitly built in, which is more representative of what is done on a real spe ctrometer.

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85 Dr. Nathan Oyler designed a simulation program in collaboration with Dr. Manish Mehta and Dr. Joanna Long when he was in Dr. Gary Drobnys group at the University of Washington. It has been used in this project to verify results against the othe r simulation programs. It also allows explicit phase cycling. The interface is a bit complicated, is not automated easily, and the software is not optimized for speed. Additionally, it is not being actively maintained, so it was not used as the main simula tor. However, it has been extensively verified by experimental data ensuring its robustness. Also, it allows the inclusion of relaxation parameters in the simulations. Initially, SIMPSON was chosen as the simulator of choice for this research as it was bei ng supported the most actively. It also had the most straightforward interface and is newer than Gamma. It is supported on both Windows and Linux and work was actively being done to get it compiled for Mac. Dr. Long, in collaboration with other members of the Drobny group at the University of Washington, had developed SIMPSON simulation routines [32]. Their code was very instructive in how SIMPSON works and how to accomplish a pulse sequence, like those in this research. SIMPSON has the capability to divide the computations for a simulation across multiple computers, also referred to as parallel computing or clustering. SIMPSON sends the computations to specially configured c ompute nodes. Initially this was seen as a very useful feature, but since the configuration was not easily amenable to public clusters, and the initial simulations ended up quite short, SIMPSONs clustering feature ultimately proved to be unimportant. SIMPSON also has problems with pulse sequences of certain lengths. These problems seem to arise from a numeric computation issue. It only worked consistently for even numbers of pulses between 2 and 22 (the maximum tried) and 5. For numbers that did not work, SIMPSON

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86 gave an error that the sequence was not rotor synchronized. The amount of time it was off by was very small, so I suspect it is an accumulation of time quantization errors. The simulations run for the last couple years have been run using spinev ra ther than SIMPSON. Support and upgrades for SIMPSON have stopped in the last couple years, but have continued for spinev. Also, spinev allows computations to be split into multiple processes on the same computer. This made some slow calculations faster and since it didnt require specially setup nodes, was easily implemented on the HPC cluster. Minimization Minimization is the process of finding the best sequence of RF pulses for a given a set of experimental constraints, such as hardware limitations or mol ecular interactions, that leads to an experimental outcome most close to ideal. Generally, experimental NMR is governed by many parameters. However, a parameter which can be controlled, such as RF, can be varied and its effects monitored. An analytical met hod for minimization is to take a differentiable function, find where its first derivative equals zero, check the second derivative to make sure it is a minimum, and test each point to see which has the smallest value. This works well for a function that i s fully differentiable. Not all experiments can easily be described analytically or are differentiable. A numerical method of minimization is to check the gradient at a specific location (the initial position), and change parameters in the opposite direct ion of the gradient to find a point with a lower function value. Repeating this process can eventually lead to a minimum. This is referred to as gradient decent. However, there is no guarantee that the minimum found is the global minimum. If the process is repeated enough times with different initial conditions, then the lowest minimum found is likely to be the global minimum, or at least close to it. Figure 3 9

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87 illustrates the difference between global and local minima. If the surface being searched is n ot smooth, the search process may never find the global minimum. Gradient decent is convenient because the gradient at each point can be found numerically and does not require closed analytical expressions. One simple method of finding the gradient is nume rical differentiation where the function is sampled on each side of the current point to determine the slope. There are many methods of gradient decent, some of which work better and some of which are easier to implement. If the function being minimized is not analytically differentiable, the function evaluation is time consuming, or the function is of high dimension, gradient decent may not be the best method of minimization. Another method of minimizing a function is by using a simplex algorithm. A simple x is a group of points in the search space. At each step of the algorithm, one or more points are moved in a direction likely to lead towards a minimum. Usually, when minimizing N variables, there are N+1 vertices to the simplex. The Matlab fminsearch function uses the Nelder -Mead Simplex method [44] The Nelder -Mead simplex (NM) method is a direct search algorithm that for a problem of N variables maintains a convex hull of N+1 vertices that surround a nonzero volume. Given a set of N+1 vertices, {x1, x2, xN, xN+1}, ordered from best function value to worst function value, {f1, f2, fN, fN+1}, each iteration of the NM algorithm returns either a new point that has a function value less than fN+1, or a set of N new points, which, together with x1, form the new simplex. Each iteration of the NM algorithm has up to 5 steps: order, reflect, expand, contract, and shrink. ORDER. Order the N+1 vertices such that f(x1) 2) N) N+1). REFLECT. Compute the point xr, called the reflection point, from Equation 3 -17. xr x ( x xN 1) (3 17)

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88 x is the centroid of the N best points, Equation 3 18. If f1 r = f(xr) < fN, xr joins the simplex. Terminate t he iteration. x 1 N xi i 1 N (3 18) EXPAND. Calculate the expansion point, xe, if fr < f1, Equation 3 19. xe x ( xr x ) ( 1 ) x xN 1 (3 19) xe joins the simplex if fe = f(xe) < fr, otherwise, xr joins the simplex. Terminate the iteration. CONTRACT. If xr is strictly less than xN+1, fN r < fN+1, calculate an outside contraction, Equation 3 20. xc x ( xr x ) ( 1 ) x xN 1 (3 20) If fc = f(xc) r, xc joins the simplex and terminate the iteration. Otherwise, perform a shrink calculation. Calculate an in side contraction if fr N+1, Equation 3 21. xcc x ( x xN 1) ( 1 ) x xN 1 (3 21) If fcc = f(xcc) < fN+1, xcc joins the simplex and terminate the iteration. Otherwise, perform a shrink calculation. SHRINK. The new, unordered list of vertex points is {x1, v2, vN+1} where vi is calculated from Equation 3 22. vi x1( xi x1) (3 22) Examples for N = 2 are shown in Figure 3 10. There are four parameters that have to be chosen for the NM method. Their standard values are = 1, = 2, = 0.5, and = 0.5 [45] Clustered Computing Clustered computing allows many optimizations or calculations to be done at the same time on parallel processors. This significantly decreases throughput time for solving problems. The University of Floridas High Performance Computing Center (hpc.ufl.edu) has more than 1800 processor cores available for research projects. Computer clusters were found to be most useful in this research for doing many optimizatio ns simultaneously rather than for speeding up individual calculations. When doing pulse optimization, each simulation depends on a previous one, so it is not possible to split the problem up to have each node doing a different set of simulations related to the same problem. Each simulation typically takes less than 30 seconds

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89 and each optimization can take 4 24 hrs. This is why it is most useful to use each node to run a different set of optimizations. When submitting a job to the HPC cluster it is importan t to understand the job queuing algorithm. A job will be queued fastest if its time and memory requirements can be accurately estimated. One way to check memory usage is to run a job and check it while it is running. Also, the email that a job can send whe n finished gives a listing of how much memory the job actually used. Estimating the amount of time a job will use isnt as straightforward as it would seem. The problem is that jobs run at slightly (and sometimes not so slightly) different speeds depending on what else a node is doing while the job is running. Generally adding 20% more time than calculated is a good rule of thumb. For the research presented here, the HPC cluster was used to do many optimizations simultaneously. This freed the authors prima ry workstation for other tasks, and allowed many more optimizations to be run simultaneously. We are very fortunate to have this cluster of computers available for our free use here at the University of Florida. The project is supported by industry partner s, university sponsorship, and particularly, individual professors writing grants that have funds set aside for the purchase and maintenance of a computer cluster, which the HPC provides for them by way of queuing priority on the number of nodes funded. Li quids Examples of Compensation by Composite Pulses Pulsed Fourier NMR has the problem of reality to deal with. Pulse lengths are never perfectly accurate. Frequencies are not all on resonance. The homogeneity of the magnetic fields involved is never perfec t. Many people have worked on designing NMR experiments to make them less sensitive to these issues. What follows is an overview of a select subset of these papers. A search on the authors will reveal many other papers that cover more topics than are prese nted here.

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90 Freeman et al. did some of the initial work showing how the introduction of a random length delay can suppress anomalies caused by acquisition being synchronous to an event [4 6] This forms the basis for most methods of suppressing imperfections. If an imperfection can be made to cycle in some manner, it can be averaged out. Phase cycling [47] is one such me thod of doing this. Pulses are tried from all the symmetric phases in a cycle so that imperfections are averaged out. There are some more complex versions of phase cycling that help to deal with imperfections in going into and out of the double quantum sta te. The idea of replacing a single pulse with multiple pulses was invented by Malcolm Levitt in 1978 in Ray Freemans group [48] This idea was given the name composite pulses to denote a group of pulses used to accomplish the same functionality as a single pulse. In the original paper, the authors replace an inversion 180 pulse with a phase of X (0) with 3 pulses, a 90(X) 180(Y) 90(X). This simple composite pulse quite effectivel y compensates for both errors in pulse lengths and off resonance frequencies. The payment is a longer pulse sequence requiring more RF power to be absorbed by the sample. Figure 3 11 shows the trajectories of a single 180 degree pulse at various frequency offsets. Note that the terminal points are in the back quadrant of the sphere. Figure 3 12 shows the terminal points as a function of offset frequency normalized to the nutation rate, / and their projection onto Iz. This gives some idea of the bandwidt h of a 180 pulse and shows how it is dependent on Figure 3 13 shows the trajectories of a 90( -X) 180( Y) 90( -X) pulse sequence at negative frequency offsets. Figure 3 14 shows the terminal points and projection onto Iz for this pulse sequence. The us eful bandwidth has been increased from that of the single 180 pulse.

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91 The Freeman group went on to explore composite pulses more fully [49] with their focus on 90 degree pulses and 180 inversion pulses and concluded It has not yet been possible to devise a composite sequence suitable for this first application, the 180 refocusing pulse. [49] In 1981 the group came closer to dealing with the issues of refocusing pulses. They found that replacing the RY( ) pulse of a Carr -Purcell spin -echo experiment with a composite pulse RX( /2)RY( )RX( /2) removes the pha se shifting on even numbered echoes [50] It doesnt suppress the phase shifting on the odd numbered echoes. The group also published a more complicated composite pulse sequence to compe nsate for inhomogeneity and frequency offset [51] Others were also in the field shortly after the Freeman group, including a description of another 3 -pulse sequence that compensates for frequency offset [52] This paper derives a method for finding composite pulses that compensate over a wider range of frequencies. Tycho later shows how using the Magnus expansion of t he deviation propagator allows pulse sequences to be derived that not only compensate in magnitude of the signal, but phase as well [53] These pulse sequences are useful for both inver sion and refocusing situations since the phase deviation of the output due to inhomogeneity or frequency offset is minimal or at least significantly lower than that of Levitts or the standard single pulses. Solids Examples In 2000, Lyndon Emsleys group decided explore numerically optimized pulse sequences [54] They set out to solve the problem of homonuclear decoupling by varying the phase of a constant R F amplitude signal. Their approach is different than what other groups have generally done, so it is worth noting. They started with the idea of optimizing the BLEW 12 decoupling sequence [55] More pulses than 12 were needed to improve the pulse sequence, but the more

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92 parameters to optimize, the harder optimization becomes since each parameter is an increase in dimensionality. Their solution was to treat RF phase as a waveform and to optimize Fourier components of the desired waveform rather than actual points in a waveform. To simplify computation they imposed a few constraints on the Fourier components to maintain known properties of good homonuclear decoupling sequences. In order to keep the RF propagator unity over a cycle, they chose to only change the first half of a cycle. The second half is just the first half with added to each of the Fourier components. This has the side effect of causing the pulse sequence to also have time reversal symmetry. Time reversal symmetry causes all the odd order terms of the Magnus expansion to vanish. From Tyckos work, this makes the pulse sequences more likely to be robust to frequency offset issues. Sakellariou et al. optimized over a range of dipolar couplings and power mismatches to achieve a pulse sequence more robust to both issues. Sakellariou ran their optimization by first generating 2x106 random sets of coefficients. The 1000 best of these sets were then chosen to be optimized using a le ast -squares steepest decent algorithm. The result of Sakellarious work is the DUMBO 1 sequence. It is a 64 step sequence based on the BLEW 12 sequence for homonuclear decoupling. They tested it using a variety of samples by observing the 13C CPMAS signal with the decoupling sequence applied to the 1H channel during acquisition. The DUMBO 1 sequence is a bit more robust to dipolar couplings and RF inhomogeneity than the BLEW 12 and FSLG sequences that they compared it with. In 2003, Dr. Emsleys group publi shed a paper on optimizing heteronuclear decoupling using the same techniques [56] Here they optimize over the residual bilinear proton -carbon terms of the effective Hamiltonian rather than just looking at the final output of a simulated

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9 3 experiment. One of the challenges was to properly model the proton bath interacting with the 13C spin. They finally settled on a phenomenological model which had to be set by trial and error between sim ulation and experiment. Their basic method of optimization was to try a set of 106 randomly generated Fourier coefficient sets. The best of these randomly generated coefficient sets were then optimized using a steepest decent procedure. They optimized over frequency offsets and proton couplings [56] The results were the DROOPY and SDROOPY pulse sequences. These sequences performed about on par with existing pulse sequences, SPINAL 64 in particular, with respect to frequency offsets. However, the DROOPY 1 and SDROOPY 1 sequences were quite a bit more robust with respect to inhomogeneity, as modeled by power misset, than SPINAL64. A second publication on optimizing heteronucl ear decoupling pulse sequences used a spectrometer for evaluation rather than a simulator [40] This is an important change since it moves from optimizing using a theoretica l model to optimizing using a specific, real system. They found that modeling the proton bath around a 13C spin was problematic, so they implemented simplex optimization using a Bruker AU program on their 500 MHz AVANCE spectrometer. They show good result s for a comparatively simple decoupling scheme. They reduced the number of parameters to 2, down from 6 complex coefficients in their previous work. The results are good across different samples for a specific magnet, probe, RF power, and MAS rate. Due to the use of an isotopically labeled test sample ([213C] -glycine) and the reduction to two parameters, the simplex algorithm converges in about 50 iterations, which take about 30 minutes for their setup. They also say that the result seems to be stable over time for the same hardware setup.

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94 Unfortunately, the results from this method are not likely to be very general across different magnets, probes, power levels, or MAS rates. If one wanted to optimize over any of these things, the length of the optimizatio n procedure would increase substantially. Even optimizing over 10 different power levels to attempt to simulate probe inhomogeneity increases the length of the optimization at least 10 -fold from 30 minutes to 5 hours. That is assuming that the simplex algorithm still converges at the same rate. From experience in my research, the simplex algorithm converges much more slowly with an increase in number of parameters. Thus, optimizing a more complicated problem, which has more parameters, would also significantly increase the amount of time required to optimize a solution. Optimizing across different magnet field strengths is a prohibitively hard problem using this method for nearly all users. It requires running experiments simultaneously on multiple magnets, the collecting and analyzing the results in a central way. With most magnets networked, this is not an impossible task, but would be very complex and very expensive. Magnet time is very valuable. When working at a user facility such as we have here at UF, magnet time varies from $6/hr for the AMRIS 500 MHz magnet in off hours to $26/hr for the AMRIS 750 MHz magnet in peak hours. Another method of optimizing pulse sequences is to simulate using optimal control theory. The idea of applying optimal control to design pulse sequences that are optimized for a particular situation was first published in 1986 with respect to MRI [57,58] The Conolly publication and a publication 10 years later [59] are probably the best fundamental papers on using optimal control in magnetic resonance. The Rosenfeld paper also shows how to use mathematical programming to solve pulse sequence optimization problems.

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95 This idea was picked up by Skinner et al. [60] in 2003 and applied to broadband excitation in liquids N MR. Khaneja et al. looked into the coupled spin problem using optimal control [61] In 2004, Dr. Nielsens lab described using optimal control to improve solid state dipolar recoupling experiments [62] This very brief JACS Communication tells of using optimal control theory to find a better pulse sequence for coherence transfer from 13C to 15N for double -cross polari zation experiments. They achieved an improvement of 53% for a 13C,15N -glycine spinning at 10 kHz with 1H decoupling in excess of 100 kHz. Unfortunately, due to the short nature of the article, there is not much information on how they did this experiment but it seemed to work for the compound they modeled in their optimizations. In 2004, Mikhail Veshtort, from Robert Griffins group, wrote an article about optimizing frequency selective pulses for both liquid and solid state NMR using his simulation progra m SPINEVOLUTION (released to the public in 2006) [63] He uses 20 30 parameters which are usually optimized using a nonlinear least -squares method after carefully selecting good soluti ons to start the optimization process. This makes it less likely for the optimization routine to get stuck in a non-optimal solution. Again, he provides the final answers, but details are limited and do not provide guidance for how the optimization procedu re may be applied to a different pulse sequence or situation.

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96 Figure 3 1. On resonance rotation. An on resonance RF field along Irot rotates magnetization from an arbitrary initial point, Iinit, an angle of around Irot to end at Iend. Figure 3 2. Off resonance rotation. The effective field, Beff, of an off resonance RF pulse, B1, is the vector sum of B1 and the offset frequency, B0. The off resonance pulse will rotate the magnetization through an angle of eff around Beff.

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97 Figure 3 3. Pauli angl e definitions. The definitions of and for rotation about an arbitrary axis using the Pauli equation method are shown. B1 is the applied magnetic field at a frequency offset from resonance by B0. Beff is the effective field felt by the spins which are then rotated by an angle of eff around Beff.

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98 Figure 3 4. Vector rotation definitions. The definitions for rotating about an arbitrary axis using the 3D vector rotation method from kinematics are shown here. K, a unit vector made up of [kx, ky, kz]T, is the effective magnetic field, Beff. The spins are then rotated by eff around K.

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99 Figure 3 5. Orientation dependence of solid state NMR. A single crystal gives a different spectra depending the molecular orie ntation. This is called chemical shift anisotropy (CSA) and is because the currents induced in the electrons around a nucleus is dependant on the orientation with relation to B0. B 0

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100 Figure 3 6. Solid state powder pattern. A powder pattern is the sum of all the possible molecular orientations weighted by their probability. B 0

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101 Figure 3 7. Spectrometer in the loop optimization. For spectrometer in the loop optimization, optimization starts with a randomly generated pulse sequence. This is evaluated on the spectrometer. The optimization algorithm determines how to change the pulse sequence to improve its quality. This new pulse sequence is then tested on the spectrometer. This is continued until the quality no longer improves. The system exi ts with an optimized pulse sequence. Random Pulse Sequence Optimization Algorithm Optimal Pulse Sequence Algorithm Converged Maximum Signal Yes No Spectrometer Signal still improving?

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102 Figure 3 8. Simulation based optimization. For simulation based optimization, optimization starts with a randomly generated pulse sequence. This is evaluated using the simulator of your choice. The optimization algorithm determines how t o change the pulse sequence to improve its quality. It goes back to the simulator where it is evaluated. This is continued until the quality no longer improves. The pulse sequence is then tested on a spectrometer (or two) to verify its capability to solve real life problems. Yes No Optimization Algorithm Maximum Function Value Algorithm Converged Optimal Pulse Sequence Random Pulse Sequence Simulation Experimental Verification Function value still improving?

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103 Figure 3 9. Minimization illustration. This shows an example of gradient decent minimization. The example function has 3 minima with one global minimum. Starting at the initial guess, gradient decent follows the gradient downwards until a minimum is found. In the example shown, the minimum found is not the global minimum. Typically gradient decent is run many times starting from random points with the expectation that eventually the global minimum will be found. X f(X) Global Minimum Local Minima Initial Guess

105 Figure 3 11. Off resonance trajectories for a 180 degree pulse. Trajectories for a 180x pulse at frequency offsets ( ) shown starting at Iz. The endpoints are marked with asterisks.

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106 Figure 3 12. Endpoints of off resonance 180 degree pulses. The endpoints for a 180x pulse at frequency offsets ( ) shown starting at Iz. The sphere shows the endpoints in 3D while the graph shows the projection onto Iz. The projection onto Iz shows the effectiveness of the pulse, disregarding phase. By = 2, no inversion is observed.

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107 Figure 3 13. Trajectories for 90 18090 composit e pulse. Trajectories for a 90x180y90x pulse at frequency offsets ( ) shown starting at Iz. The endpoints are marked with asterisks. This more complicated pulse sequence brings the final state of the magnetization closer to -Iz than just the 180.

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108 Figure 3 14. Endpoints for 9018090 composite pulse. Endpoints for a 90x180y90x composite pulse at frequency offsets ( ) shown starting at Iz. The usefulness of the composite pulse does not extend much past = 1, but is much flatter than the single 180 pulse, giving it a wider useful bandwidth.

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109 CHAPTER 4 OPTIMIZATION OF RF E XCITATION PROFILES The general methodology of optimizing pulse sequences followed in this dissertation was shown in Figure 3 6. Optimization starts with a randomly generated pulse sequence. For all the pulse sequences optimized, the initial phases are set randomly. For some pulse sequences (inversion and refocusing pulse sequences) the lengths of the pulses are also initially set randomly. For other pulse sequences (suc h as DRAWS, which has to be rotor synchronized) the pulse lengths are fixed. The randomly generated pulse sequence is tested via an NMR simulator to give a measure of how well the pulse sequence works. A minimization routine (usually fminsearch from Matla b) then continues by algorithmically changing the free parameters (phases and possibly the pulse lengths) in such a way that the pulse sequence evaluates better. This continues until the minimization routine cannot improve the pulse sequence above some thr eshold. The routine then stops optimizing that pulse sequence and generates a new random starting point, continuing around the optimization circle again. This is repeated as many times as resources allow. The best pulse sequences obtained are then tested o n a spectrometer to verify that they work in real life. Three types of pulse sequences were optimized for this work: inversion, refocusing, and DRAWS. Optimizing Inversion Pulse Sequences Introduction An ideal inversion pulse sequence takes magnetization t hat is along the +Z axis and rotates it to the Z axis. These are commonly used in inversion recovery studies to determine T1, the constant for spin -lattice relaxation. For typical molecular species and NMR spectrometers, inversion pulse sequences are impe rfect. One aspect of their imperfection is that they dont invert

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110 all frequencies equally. For example, take a single 180 pulse which would be 10 s long for a 50 kHz RF field. This is a very simple pulse sequence that only has one pulse besides the readout 90 pulse, shown in Figure 41. A frequency from the center frequency will experience a nutation rate, eff, as shown in Equation 41 and explained in more detail in chapter 3. eff (nut)2 ( )2 (4 1) Another way to state it is: offset frequenci es will experience a faster nutation rate than the center frequency. They will also rotate around an axis that is the vector sum of the nutation axis and the offset frequency along the Z axis as discussed in Chapter 3. The 10 s pulse that gives perfect in version at the center frequency will not give perfect inversion at an offset frequency. It will overshoot by some amount. This can be seen in Figure 4 2 where the trajectories for 0.5 are shown. Figure 4 3 shows where the bulk magnetization ends up after a 180 pulse around X. This problem can be solved with better pulse sequences for inversion [51,52,64] The results using SPINEVOLUTION [43] (hereafter referred to as spinev) at a spin rate of 10 kHz and power of 30 kHz are shown in Figure 4 4 for some of these pulse sequences. The pulse sequence by Keniry et al (magenta in Figure 4 4 starting with a pulse length of 38) [64] gives the wide st bandwidth so it is used as a comparison in this work. The composite pulse by Bai et al. (yellow in Figure 4 4) [65] is also a good comparison pulse sequence because it uses pulse leng ths that are not integer multiples of 90. Experimental verification of these pulse sequences were run to make sure that the spectrometer setup was correct and the simulations agreed well with experiment before optimizations were run. Starting with the single 180 pulse, there was a large discrepancy between the experiment and simulation. The lower offset frequency side of the experimental data

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111 drooped below the simulated data. After trying a variety of things, it was determined that the problem was that t he recycle delay was too short. Examples of data for different recycle delays are shown in Figure 4 5 and shows that a recycle delay of 10 seconds is sufficient. Further testing showed that 7 seconds of recycle delay were adequate for adamantane. Experimen tal data compared to simulated data for a single 180 inversion pulse are shown in Figure 46 for a few power levels. A representation of the lengths and phases of the pulse sequence by Keniry et al. is shown in Figure 4 7 [64] Note that this pulse sequence uses 558 degrees, which is just over three times as long as a single 180 pulse. A comparison of experimental to simulated data is shown in Figure 4 8 for three power lev els for an adamantane sample 3.7 mm long. These two examples showed that experimental and simulated data match quite well for the low E probe described in Chapter 2. This is likely due to the high homogeneity (96% on 13C and ~100% on 1H) of the RF and the modern spectrometer used (Bruker Avance II). Using spinev, I have optimized pulse sequences to give a better inversion profile than those in the above references when used in ssNMR. Methods Inversion pulse sequence optimization started with testing a 180 pulse sequence over a range of 100 kHz frequency offsets. This was done both in simulation using spinev and experimentally on a 750 MHz spectrometer. The idea of finding an optimal pulse sequence is to use multiple pulses, with differing lengths and pha ses to invert a larger range of frequencies more evenly. Optimizations were run with one pulse through 8 pulses with the phase and lengths unrestricted. Minimization was done using Matlabs fminsearch function. The basic procedure for optimizing is as follows. The random number generator in Matlab is reset to something random, usually 100*clock. This is important since the random number generator is initialized to

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112 the same point each time Matlab is started. If it isnt reinitialized, the set of random numbe rs it generates will be the same every time it is run. A set of random pulse lengths and phases is generated. Both are represented in degrees between 0 and 360. This is because fminsearch works better if all of the parameters it is varying are on the same order of magnitude. fminsearch is run starting at this random initialization. The process is repeated as many times as possible. Evaluation of an inversion pulse sequence is done by the function spinev_eval_inv_dly.m. This function separates out the pulse length parameters from the pulse phase parameters. If desired, it can add an intermediate pulse between the specified pulses that has a phase halfway between its adjacent pulses. The idea was to model phase slew, which has not turned out to be a significa nt parameter in fitting the data. Next, this function writes a pp file that contains the pulses, phases, powers, and frequency offsets for the trial inversion pulse sequence. Doing a system call to spinev follows this. The function takes advantage of the n ew macro feature introduced in spinev 3.3 that allows variables within a pulse program to be specified on the command line when that program is called. This is how the pp file, frequency offsets, and power offsets are specified. Also, the eval function mak es use of the new spinev feature of having the results returned to the command line. Matlab reads the command line return and thus saves a file write and read cycle, which tend to be slow. The end of the eval function returns the sum of the polarization di vided by the number of simulations done. This normalizes the results to be 1 for perfect inversion. Normalizing the result this way makes for easy comparison to an ideal inversion pulse sequence. The eval function also checks to make sure that the spinev expiring warning does not cause problems and can add an extra multiplier (usually 1 if used) in case the function is used for evaluating something other than an inversion pulse sequence (this same function is also used in refocusing pulse sequence optimiz ation).

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113 All of this is done many times (hundreds to thousands) for different numbers of pulses. In order to get other work done while this is happening, the optimizations are usually run on the HPC cluster. The best solutions are then written as a Bruker pulse program and tested on a spectrometer using adamantane (Acros Organics) as the sample. Comparisons were then made between the simulated results and the experimental results to determine if the simulation was actually making sense. One somewhat amusing observation was over fitting. To optimize for broad spectral width, points were initially optimized from 100 kHz to +100 kHz every 50 kHz. When the intermediate points were tested via simulation, it showed that the optimization process had only minimized the signal at the points where the optimization was tested, and the other frequencies were quite high as shown in Figure 4 9. This proves that it is important to sample over the region of interest and to double check how well solutions generalize. Most of the optimizations were done with a 10 kHz step in frequency offset, but some were done with a 1 kHz step to see if the result would be a flatter bandwidth. Initially, pulse sequences were optimized over both power offset, to model power missets and inhomogeneity, and frequency offset. It is important to keep in mind that there are different ways to look at power offsets. One way is to change the transmit power (nutation rate) but not the pulse length. This simulates an incorrectly calibrated pulse length. Another way to simulate the same thing is to change the pulse length, but not the power level. This way is not how we typically think about modeling inhomogeneity. The third way to look at power offset is to have the power and pulse length scale together. This is important to think about in case the pulse sequence is optimized for a specific power setting or MAS rate. This became particularly important when fitting the experimental data. Initially, the experimental data was run at a

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114 correctly calibrated nut ation rate of 62.5 kHz while the simulations ran at 50 kHz. In trying to match simulation and experiment, there was a 0.8 frequency offset scaling factor due to the fact that 50 divided by 62.5 is 0.8. Once that issue was solved, the experimental data fit the simulation data quite well. Optimizing over different power levels turned out not to be necessary for using pulse sequences on the 750 MHz magnet with the Low -E MAS probe. The homogeneities of the B1 fields on this probe are high enough that inhomogene ities do not need to be modeled. As the optimizations continued, two modifications to the method were added. First, instead of just trying to minimize the average output (projection on to Iz), the system was changed to minimize the sum -squared error betwe en a desired frequency offset profile and the simulated frequency offset profile. This allowed arbitrary profiles to be generated. The second modification to the method was to use constrained optimization as implemented in Matlabs fmincon function. This was done as an attempt to prevent composite pulses with pulse lengths shorter than the spectrometer can actually generate. This changed the minimization method from Nelder -Mead simplex to a sequential quadratic programming method. This is a conjugate gradi ent decent type method which uses an perturbation method of calculating the gradient for functions lacking a gradient function. Setting the amount of perturbation turned out to be critical in getting this method to work. It needed to be increased to be lar ge enough to see a gradient but the results were no better than the unconstrained optimizations. Results The pulse lengths and phases of the best pulse sequence from unconstrained optimization using the Nelder -Mead method are shown in Figure 4 10. This com posite pulse is just over 6 times the length of a single 180 pulse. Note that all of the pulse lengths and phases are arbitrary,

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115 i.e. not equal to an integer multiple of 90. Figure 411 shows a comparison of a single 180 pulse, the pulse sequence by Ken iry et al., and my optimized pulse sequence at 32 kHz RF power. The correlation between simulation and experiment is quite good and the bandwidth over which the magnetization is inverted is also quite good. My optimized composite pulse has a wider bandwidt h, slightly higher ripple, and a longer RF excitation than the pulse sequence by Keniry. Figure 4 12 shows a comparison of the inversion data for a sample 3.7 mm long and a sample that is 11.7 mm long. The homogeneity was ~96% for the 3.7 mm sample and ~76% for the 11.7 mm sample. While both sample lengths match the simulation relatively well, with the longer sample does not fit quite as well. This is to be expected since the longer sample has more spins resonant at frequencies farther from the transmission frequency. Optimizing Refocusing Pulse Sequences Introduction Inversion pulse sequences take bulk magnetization that lies on the +Z axis and move it to the -Z axis. There are times when instead it is desired to take magnetization that has precessed in the XY -plane and move it to the opposite side of the XY -plane. This is typically called a refocusing pulse. When an onresonance signal is observed in the rotating frame, it is stationary in the XY plane (ignoring any relaxation). An off resonance signal will precess around the XY plane at a rate equal to the how far off resonance it is. This i s the cause of first order phase errors when looking at a spectrum that encompasses a broad range of frequencies. One method to remove these phase errors is to use a spin -echo pulse sequence. The importance of the spin -echo in modern NMR techniques can ha rdly be over emphasized [35] A typical spin -echo sequence consists of a delay, a 180 refocusing pulse, and a second delay of Figure 4 13. In ssNMR

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116 typically equals a rotor period minus half the length of the 180 pulse. The idea for this pulse sequence is that the signals that are above the resonance frequency will be moving away from resonance in one direction and those below resonance in the opposite. If a 180 pulse inverts the whole XY -plane, both of these signals will now be moving back towards their starting point. At the end of the second all the signals will be back where they started with no first order phase errors, Figure 4 14. The di fficulty is that signals that are not on resonance do not experience the same effective pulse length as those on resonance. The goal of optimizing refocusing pulses is to overcome this problem by finding a composite pulse sequence which flips a much broade r range of frequencies 180 degrees. This problem has been explored, particularly in liquid state NMR. Examples include: [48 51,53,66,64,65] Similar to the inversion pulse sequence problem, pulse sequences that are optim ized for liquid -state NMR do not always transfer over to ssNMR directly. The simplest refocusing pulse, the 180 pulse, can be used as an example, Figure 4 15. In a liquids simulation, the signal strength goes through a series of beat patterns of fast osci llations that increase in strength as the resonance offset increases as shown by the blue trace. The green trace shows the same simulation using the same RF power, but now in a solids sample with a MAS rate of 10 kHz. The beat pattern has changed to a slow er oscillation of increasing strength. It turns out that this oscillation frequency for the solids signal is dependent on both MAS rate and RF power level. Figure 4 16 shows a series of simulations across 4 power levels. The oscillations increase in freque ncy with increased RF power. The oscillations decrease in frequency with increased MAS rate, Figure 4 17.

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117 Using spinev, I have optimized pulse sequences to give a better refocusing profile than those in the above references when used in ssNMR. Methods The first big problem is coming up with a simulation program that accurately describes the refocusing problem. Spinev provides the capabilities to make runtime chosen pulse lengths, but the method was not straightforward at first. An example refocusing pulse s equence input file is shown in Figure 4 18. The spin system shown approximates adamantane and the pulse sequence has 3 pulses. The first and last are the delays, The middle pulse is the composite pulse, specified by the $P replaced by the name of the fi le containing the composite inversion pulse sequence using the macro command line option. The foffs scan_par is used to simulate across the different offset frequencies. The $F is also replaced using the macro command line option. It has the form of low: step:high frequency offsets. The $P is the range of powers to simulate over, is also replaced using the macro command line option and has the same form as the frequency offsets. Due to the high homogeneity of the probe used in this research, the optimizat ions were only done at one power level which models perfect homogeneity. Figure 4 19a shows a typical composite pulse input file (the name of which replaces the $P in Figure 4 18). The first column is the pulse lengths, the second is pulse powers, the thi rd is pulse phases, and the forth is pulse frequency offsets. Figure 4 19b shows the commands used to run a refocusing experiment using spinev. Initially, differences arose between the simulation data and the experimental data. The problem turned out to b e the method of automatically calculating the lengths. The initial attempts at calculating them inadvertently turned on the RF during them in the simulations. When attempting to model proton coupling during the s the program was rewritten with all the

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118 values hard coded. This greatly improved the match between simulation and experiment. Attempting to reautomate the calculations revealed the location of the error being that the power was on during the s. Most of the methods for optimizing refocusing pul se sequences are very similar to those used in inversion pulse sequences. A generic pulse sequence program is written for spinev. A Matlab master program is written (very similar to the one for inversion) to run fminsearch, which varies the pulse lengths a nd phase for N pulses. N was varied from one to ten and the optimizations were run on the HPC cluster. Since the signal across various frequencies seemed to fluctuate quite a bit, the frequencies were run in 2 kHz steps initially for optimization. This see med like a good compromise between calculation time and sampling width for optimizations. Results The results for three refocusing pulse sequences are shown in Figures 4 20 to 4 22. Figure 4 20 shows the experimental and simulated results for using a sing le 180 degree pulse for refocusing. The simulation and experiment match quite well. This data was taken with an RF power of 51.2 kHz and a MAS rate of 10 kHz across an offset frequency range of +/ 50 kHz. Figure 4 21 shows data with the same settings for a composite refocusing pulse developed by Bai et al. [65,66] It was optimized using simulated annealing to be phase -distortionless composit e pulses. They were demonstrated as inversion composite pulses, but being phase distortionless, they should work well as refocusing pulses too [53] and the simulation supports this. The experimental data does not fit as well as the 180 data does. This may be the result of a slight misset of the spectrometer either in specifying the true resonance correctly or in calibrating the length of the pulses correctly. Even with it not fitting well, the response is far superior to that of a 180 pulse. Figure 4 22 shows a composite pulse obtained through the research presented in

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119 this paper. It is marginally longer than the pulse sequence by Bai et al., 1224 degrees vs 1166 degrees. The simulation and experimental data fit better than the data in Figure 4 21, but still not as well as that for the 180. The more complex composite pulses in a more complicated situation provide for more chance of divergence between simulation and experiment. A comparison of all three pulse sequences is shown in Figure 4 23. To numerically compare these composite pulses, the average value across a frequency offset range of +/ 2 is compared. The 180 has an average value of 0.4422 for simulation, the composite pulse by Bai et al. has an average value of 0.5598 for experimental data and 0.5893 for simulation, and the composite pulse optimized for this research has an average value of 0.8594 for experimental data and 0.8910 for simulated data. Both of the composite pulses are better across the frequency offsets than a 180 pulse, with the composite from this research being the best. If comparing across only +/ 1 the tables turn a bit. Bai et al.s pulse turns out to be better than the pulse sequence from this research over the narrow range. Both composite pulses are still better than the 180. The composite pulses do come at a cost. Bai et al.s pulse sequence is 6.5 times as long as the 180 and the composite from this research is 6.8 times as long as the 180. This is a tradeoff that has to be understood well when using composite pulses. They do not always function well as straight drop -in replacements for a single 180 pulse. Figu re 4 24 shows a comparison of the pulse sequence optimized for this research at two different sample lengths, 3.7 mm and 11.7 mm. The difference is much more drastic here than with the inversion pulse sequences. The longer sample matches the simulation not iceably worse than in the inversion pulse sequences. The simulation assumes perfect homogeneity and neither of the composite pulse sequences were optimized to reduce the effects of inhomogeneity.

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120 Optimizing the DRAWS Pulse Sequence Introduction The pulse s equences being optimized so far are simple pulse sequences that are building blocks for much more complex experiments. One of the main pulse sequences used in the Long lab is the DRAWS pulse sequence [30] Figure 4 25, therefore this was the first pulse sequence optimization was attempted on. This pulse sequence is designed to determine internuclear distances in doubly labeled samples via windowless dipolar recoupling. In sim pler terms, this means that the distance between two 13C labeled amino acids in a peptide or protein can be measured. Windowless means that it is a pulse sequence where the transmitter stays on during the whole excitation period. Some pulse sequences have periods where the transmitter is turned off and the spins are allowed to freely precess for a period of time. The buildup form of the DRAWS pulse sequence does not have any free precession times. However, once DRAWS has been used to build up double quantum (DQ) coherence, it is possible to let the DQ coherences evolve before running DRAWS in reverse to bring the signal back to single quantum states where it can be directly observed. This has been shown to be quite useful in finding backbone torsion angles o f peptides [31] It has also been used by our lab to help illuminate the structure of a peptide mimic of lung surfactant protein B, one of the proteins essential to lung function [67] The theoretical maximum efficiency for DRAWS varies depending on the particular sample being run, but they average in the mid to low forty percent range [32] However, the experimental efficiencies are lower, in the high twenty to low thirty percent range [32] It would be very nice if the pulse sequence could be optimized to make it easier to achieve the theoretical maximum efficiency and possibly increase this theoretical maximum. This could involve optimizing a pulse sequence for each specific sample, but idea lly, a more general result could be

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121 obtained. It might also be handy to optimize other double quantum recoupling experiments to make them easier to setup to achieve their maximum efficiency. Double quantum recoupling efficiency (DRAWS in particular) diminishes as the static field, B0, strength increases due to interactions of the increased size of the CSA [32] This counteracts the signal increase from the improved sensitivi ty these higher fields bring. It would be nice if a pulse sequence could be found that is not so sensitive to the increase in static field strength. These recoupling experiments (again, DRAWS in particular) are also quite sensitive to B1 inhomogenieties. R educed homogeneity noticeably reduces the DQ efficiency. It would be nice if a pulse sequence could be found that is also more tolerant to inhomogeneity. The goal of this dissertation section was to optimize the DRAWS pulse sequence to improve its efficien cy and robustness with respect to B0 field strength and inhomogeneity of the B1 field. Methods Several methods of optimizing the DRAWS pulse sequence were tried. The bulk of them, particularly at first, used the SIMPSON simulator [42] The original DRAWS pulse sequence is shown in Figure 4 25. Each basic R group consists of 10 pulses. Eight of them are 360 degrees in length (measured in nutation distance) and two of them are 90-degree pulses, Figure 4 26. The first method was to use Fourier components to define a pulse sequence in the manner of Sakellariou et al. [54] The method assumes a windowless experiment at constant amplitude RF. The only variable factors are the phases throughout the excitation. Rather than treating the phase of every pulse as a variable, which could be hard to optimize if there were hundreds of pulses, they reduced the n umber of variables by treating the phase throughout the experiment as the waveform described by a Fourier series. The parameters to optimize are the complex Fourier

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122 coefficients. They chose to use 6 complex coefficients, which leads to 12 parameters. I tri ed this Fourier component optimization method without successfully finding pulse sequences with better properties than the original DRAWS pulse sequence when I first started on the project of optimizing pulse sequences. It might be worth revisiting in the future with the simpler experiments currently under development. The next optimization method replaced the R group with 10 equal length pulses. The length of each R group was still R, one rotor period, and the same supercycling of the 4 R groups, R Rbar Rbar -R, was used. The power level was also fixed at the same level that would have been used for a regular DRAWS sequence. The new R group also maintained reverse symmetry, so that only the first half of the R group was optimized. The second half of the R group was simply a reflection of the first half. Some optimizations were done without this constraint, but they never produced pulse sequences even as good as the original DRAWS pulse sequence. The optimization procedure searched for the phases for the fir st half of the pulse sequence (the second half used a reflection of them) that produced the maximum signal. The buildup curve was done at each optimization step out to 10 supercycles and the maximum value in those 10 supercycles was maximized. This method worked well and was used for the bulk of the optimizations done on DRAWS. The last method of optimizing DRAWS used the original pulse lengths from DRAWS, rather than 10 equal length pulses. Just the phases for each pulse were varied to see if a better set of phases could be found. Results Both the experiments optimized in SIMPS ON and in spinev were run on the 750 Mhz spectrometer using the low E MAS probe. Neither sets of experimental data matched the

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123 predicted simulation data in shape or intensity. A representative example of a pulse sequence optimized using spinev and pulse le ngths the same length as the original DRAWS is shown in Figure 4 27. The simulation and experimental results are shown in Figure 4 -28. The simulation showed that there should be an increase in signal by about 30%, but the experimental results showed a decr ease in signal to about 60% of the original DRAWS signal. This set of data also gives some clues about how optimizing this kind of pulse sequence could be improved in the future. Note that the original DRAWS data does not match up well between simulation a nd experiment. Tentative results suggest that matching the theoretical spin system to the experimental spin system better could reduce this discrepancy. It was originally hoped that the optimized pulse sequences would be robust across variations in the spi n system. Experimental data suggests otherwise. In working on the inversion and refocusing problems, a method of optimization emerged. Start by running a simulation of the experiment. Next run the experiment. Try to fit the experimental data with the simul ation. It maybe helpful to run optimizations of the experiment, run the experiments and try to fit both the original and optimized data with simulation. Once the simulations and experiments match well, move on to more optimizations and better optimization methods. In the future, attempts should be made to find simulations that accurately describe the experimental results from implementing the optimized pulse sequences.

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124 Figure 4 1. Inversion pulse sequence. An inversion pulse sequence rotates the magnetization from along Z 180 degrees to be along Z. In order to observe this signal, a 90 degree pulse is used to rotate the magnetization back to the X Y plane. To test the frequency robustness of an inversion pulse, the inversion pulse is transmitted off resonance, but the 90 degree pulse is kept on resonance. 90 180

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125 Figure 4 2. Inversion trajectories for 180 degree pulse. Single 180 pulse around -X trajectory paths for a spin on resonance (green), at +0.5 (red) and 0.5 (blue). A of 0.5 is equivalent to a frequency offset of 30 kHz for an RF power level of 60 kHz. This simulation does not model crystallites or magic angle spinning. In other words it assumes a liquid.

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126 Figure 4 3. Endpoints for 180 degree pulse with varying fr equecy offset. Endpoints of a single 180 pulse around -X while varying the A 0.5 as shown in Figure 4 2 would be in either the cyan or yellowish green regions. This simulation does not model crystallites or magic angle spinning. In other words it assumes a liquid.

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127 Figure 4 4. Simulations using SPINEVOLUTION of various liquids composite inversion pulses simulating an adamantane like solid spinning at 10 kHz. A regular 180 pulse around X is in blue. References for the rest of the sequences is as follows: green [48] red [49] cyan [51] magenta [64] yellow [65,66]

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128 Figure 4 5. Finding a useful recycle delay. Initial f experiments did not match simulation well. This was because the recycle time for the sample used (adamantane) was too short. Here are s ome examples of what the results are for various recycle times. It turns out that a recycle delay of 7 seconds is usually enough for adamantane.

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129 Figure 4 6. Comparison of experimental and simulation data (SPINEVOLUTION) for a single 180 inversion puls e. The pulse sequence was a 180 followed by a 90 to bring the bulk magnetization back into the X Y plane for observation. The transmit frequency offset was only changed on the 180 pulse. The experimental data is from integrating the adamantane resonance at 38.48 ppm for a sample length of 3.7 mm.

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130 Figure 4 7. Composite inversion 180 pulse showing the lengths and phases of the pulses. This pulse sequence was developed by Sanctuary et al. [68,64] via the series expansion of the offset angle method.

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131 Figure 4 8. Comparison of experimental and simulation data for a composite inversion pulse. This pulse sequence was developed by Keniry and Sanctuary [64] via the series expansion of the offset angle method. Note how flat the response is in the middle. Experimental data is integration of the adamantane peak at 38.48 ppm for a sample length of 3.7 mm.

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132 Figure 4 9. Optimization undersampling. The pulse sequence was optimized by minimizing the signal at the points indicated by the red circles. The signal is nicely minimized at these points, but not in between which is an example of over fitting or maybe under fitting. A tighter grid of points is needed. Since the homogeneity of the 750 MHz probe is so high, optimizing over different power levels is not needed. Therefore, all the time can be focused on optimizing over more points at the desired power level (usually 50 kHz).

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133 Figure 4 10. An optimized composite inversion 180 pulse showing the lengths and phases of the pulses. This composite pulse was optimized by the author during this research using the Nelder Mead simple x method and spinev. This pulse sequence is just under 6 times the length of a single 180 pulse.

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134 Figure 4 11. Comparison of various inversion composit pulses. This figure compares all three pulse sequences discussed so far at the lowest power level. Th e lowest power level has the narrowest bandwidth. A standard single 180 pulse is in blue. The composite by Keniry and Sanctuary [64] is shown in green and the pulse sequenc e optimized for this research is shown in red. Note that the optimized composite pulse has a wider bandwidth at a minimal expense of greater ripple.

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135 Figure 4 12. Inversion homogeneity match to simulation. The match between simulation (green line) and ex periment (Xs) is not as good for longer samples as it is for shorter samples. This example is for an optimized pulse sequence at 52 kHz RF. The homogeneity of the 13C channel for the 3.7 mm sample is ~96% and for the 11.7 mm sample is ~76%.

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136 Figure 4 13. Refocusing pulse sequence. A refocusing pulse sequence begins by rotating the magnetization into the X -Y plane. Following that, there is a delay of where is equal to a rotor period, R, minus half of the length of the 180 refocusing pulse. Another follows the 180 pulse before acquisition commences. Figure 4 14. Refocusing explaination. In the rotating frame of reference, spins at a higher frequency than the reference frequency will rotate away from their starting position (X here) in one direction (red), while those at a lower frequency will rotate i n the opposite direction (green). A refocusing pulse inverts the X Y plane so the resonances exchange positions while retaining their direction of rotation. At some time, after the refocusing pulse, the spins will all be aligned along their starting position again. Refocus Pulse 90 180 R R

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137 Figure 4 15. Refocusing comparison between liquids and solids. Simulations of a liquids refocusing experiment and a solids refocusing experiment at 10 kHz MAS show how different the results can be between the two cases. Both use the same values for and a spin system that approximates adamantane.

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138 Figure 4 16. Solids refocusing power response. The response of a refocusing pulse is sensitive to both the MAS rate and the power of the applied pulse. This figure shows simulations of how the response varies according to power level for a solid sample with spin parameters that approximate adamantane with a MAS rate of 10 kHz.

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139 Figure 4 17. Solids refocusing MAS rate response. Simulations of a 180 refocusing pulse around +X at various MAS rat es using a spin model that approximates adamantane show how the response varies with MAS rate.

141 Figure 4 19. spinev input pp file and commandline call. A) A typical pulse input file for a spinev main program such as that shown in Figure 4 19. The first column is the length of the pulses in microseconds. The second column is the power for each of the pulses in kHz. The third column is the phase of the pulses in degrees. The last column is the frequency offset for the pulses in Hz. B) The command line argument used to run the scripts in Figure 4 19 and 4 20a. It sources .profile because the terminal MATLAB loads does not automatically do this. .profile updates the paths to include spinev. The t argument returns the output to the command line where matlab reads it in. The macro commands do text replacement in the .spv file. re makes the script only return the real part of the data. -split2 splits the process into two threads for faster execution on a computer with at least 2 processor cores. The renice10 command nices the threads so that they dont take over the computer. 27.848861 32.258065 253.819629 0.000000 23.164910 32.258065 154.993246 0.000000 10.180519 32.258065 328.578250 0.000000 23.384791 32.258065 153.043209 0.000000 9.007919 32.258065 236.164760 0.000000 4.779880 32.258065 309.853269 0.000000 13.310008 32.258065 305.223512 0.000000 0.016393 32.258065 196.789120 0.000000 *** Duration Pwr Phase Offset *** *** refocus_opt.pp *** *** Automatically created by /Users/mcnese/Seth/bin/write_spinev_pp *** *** Created at 08 Jan 2009 09:22:24 *** source ~/.profile; spinev refocus.spv t macro \ $P="refocus_opt.pp \ macro \ $F= 100.00:10.00:100.00 macro \ $N=50.00:1.00:50.00 re split2 renice10 a) b)

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142 Figure 4 20. Simulation and experiment for a single 180 refocusing pulse The simulation and experimental data for a 180 refocusing pulse match very well. This data is at 51.9 kHz RF power and 10 kHz MAS rate. The average value across of +/ 1 for the experimental data is 0.7246 and 0.7580 for the simulation data. This gives some idea of the refocusing ability of this pulse sequence. The simulated average value across a of +/ 2 is 0.4422.

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143 Figure 4 21. The refocusing data and sim ulation for the composite pulse by Bai et al. [65] The simulation and experimental data dont fit as well as the 180 shown in Figure 4 20, but it shows a remarkable improve ment in bandwidth from the 180. The average value across of +/ 2 for the experimental data is 0.5598 and 0.5893 for the simulation data. From Figure 4 21, the 180 has an average value of 0.4422 over +/ 2 so this pulse sequence is definitely bette r than just a 180. Over +/ 1 this composite pulse has an average value of 0.9330/0.9696 experimental/simulated which is significantly better than just a 180 pulse.

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144 Figure 4 22. The simulation and experimental data optimized in this research. The a verage value across of +/ 2 for the experimental data is 0.7490 and 0.8392 for the simulation data. This gives some idea of the refocusing ability of this pulse sequence. Over +/ 1 this composite pulse has an average value of 0.8594/0.8910 experi mental/simulated so this pulse sequence is significantly better than just a 180 pulse for both frequency offset ranges. The composite pulse in Figure 421 does better over the narrower range, but this pulse sequence does better over the wider frequency off set range.

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145 Figure 4 23. A comparison of all three refocusing pulses. The bandwidth of both composite pulses is better than that of a single 180.

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146 Figure 4 24. Homogeneity and refocusing pulse simulations. Comparing experiment (Xs) to simulation (lin es) for long samples (11.7 mm green) as well as short samples (3.7 mm blue) for a composite pulse sequence optimized in this research shows that just like for the inversion pulse sequences, the match gets worse. Modeling inhomogeneity may help reconcile th e differences.

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147 Figure 4 25. The DRAWS pulse sequence. The DRAWS block is repeated n times where n usually is between 1 and 10. R -bar is an R group with the phases shifted by 180. The Z filter at the beginning ( /2 -delay /2 over 2R) and the echo at the end (the pulse in the middle of 2 R) are both not critical and were usually not implemented for this research. The first DRAWS group is the excitation part of the sequence which creates the double quantum (DQ) coherence. The second DRAWS group converts the DQ coherence back into single quantum (SQ) for observation. 2 CP CP 2 2 2 R DRAWS 2 n 2 DRAWS n 2 R CW Decoupling R R R R 2 x2 -x 2Y 2 x2 x2 -x2 -x2 -x2 x 2Y 1H13C R t2

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148 Figure 4 26. The original DRAWS R group pulse lengths and phases for comparison with the optimized DRAWS in Figure 4 27. Figure 4 27. The optimized DRAWS R group pu lse lengths (the same as original DRAWS) and phases.

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149 Figure 4 28. DRAWS experimental and simulation data. An example of simulation (lines) and experimental (xs) data for regular DRAWS (blue) and an optimized form (red) is shown where the data is normalized to the magnitude of the regular DRAWS for both simulation and experiment. The regular DRAWS experiment versus simulation do not match. This is most likely due to differences between the simulated spin system and the experimental spin system.

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150 CHAPTER 5 CONCLUSIONS AND FUTU RE DIRECTIONS Conclusions This research presents hardware and software solutions to many of the problems facing biological ssNMR at high fields. The low E 750 MHz MAS probe was thoroughly characterized in order to determine the RF efficiency of each channel, maximum achievable B1 fields, homogeneity of the B1 fields, isolation between channels, stability at high power, RF induced sample heating, frictional heating under MAS, spectral linewidths, and signal/noise on standard c ompounds. Under normal operating conditions, a 1H B1 RF field of ( 1 kHz and homogeneity (810/90) of 93% can be obtained with a sample length of 8.4 mm corresponding to a volume of 80 L. With a higher power amplifier, we should be able to excee d 110 kHz decoupling fields based on bench measurements. 13C B1 RF fields greater than ( 1 kHz with a homogeneity (810/90) of 70% are routinely observed for this sample length; the 13C B1 homogeneity can be increased to 89% with a 6.7 mm sample length. Under full 1H decoupling for long periods of time, sample heating due to the high RF field is minimal even for samples containing physiological levels of salt. We have not noticed any sample degradation in heat sensitive samples after extensive exp erimentation. The power handling characteristics, B1 fields, and homogeneities make this an ideal probe for applying the full range of MAS solid state NMR experiments, including sequences which use extended periods of continuous RF pulsing on both channels to biological samples which are inherently dilute. This probe is providing high quality data to further scientific research of biological problems. In particular, the mechanism of lung surfactant protein B is currently being studied. Other studies have a lready been run using this probe, including attempts to analyze different Brazilian soils.

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151 A system for optimizing pulse sequences for ssNMR was also developed, demonstrated, and is running. This system was demonstrated on the two standard pulse sequences used to test pulse optimization systems: the inversion experiment and the refocusing experiment. In both cases, pulse sequences were derived which had a wider bandwidth than existing pulse sequences and had extremely good agreement between experiment and s imulation. These pulse sequences should be useful in maintaining high signal strength and phase coherence in future research. The methods of optimization and verification allow them to be easily extended to more complex situations in future research. The c ombination of the new probe and the method for optimizing pulse sequences for use at higher fields opens many opportunities for new research on biological solids. Future Directions Probe Development A static low -E probe for a 360 MHz magnet in chemistry is currently being built. It will provide a sturdy workhorse probe for the 360 magnet since all the other probes are older and less efficient than this probe will be. It serves as a platform for us to redesign our circuits for implementation in narrow bore m agnets. Two improvements to the probes current design should be considered. First, use zero susceptibility wire to reduce the foot in spectra. Second, make the 13C coil longer to improve its homogeneity in order to make use of the whole sample volume. This should be feasible since the cavity in the stator is long enough to fit a longer solenoid and LGR. The next logical steps in the development of new low E MAS probes is the addition of a third RF channel and their redesign for narrow bore magnets. A triple resonance probe would allow simultaneous excitation at 15N, 1H, and 13C frequencies. This is very useful in the study of biological solids. Preliminary design work has been done on this front for a 750 MHz triple

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152 resonance MAS probe. A narrow bore low -E M AS probe is the ultimate goal since most of the NMR magnets are narrow bore due to issues of cost and siting. Narrow bore means the diameter of the bore is 51 54 mm versus the 89 mm bore that the 750 MHz magnet has. Pulse Sequence Optimization Both invers ion and refocusing composite pulses need to be implemented into more complicated experiments to demonstrate their usefulness. The usual process for pulse sequence development is to develop a solution, test it on a standard sample (adamantane with the pulse s at a frequency offset is generally used), and then demonstrate its usefulness on a more complex sample. This work has been started for the pulse sequences developed in this research, but still in progress. Alternate methods of optimization should also be implemented. The basic framework that was developed for this research is amenable to other optimization methods. One potential avenue is to use genetic algorithms to find optimal pulse sequences. Additionally, Niels Nielsons group in Denmark recently re leased a new version of SIMPON which has their optimal control method built in [69] It would be instructive to get a system running here at UF using this new version to see if it compares favorably with the optimization method developed in this research. Getting optimized DRAWS running would be a big boost to the research here at UF. Dr. Long uses it heavily in the research on lung surfactants. Lung surfactant samples are dilute an d not always stable for long periods at high temperature, so being able to run DRAWS experiments more quickly would help to ensure sample integrity and also allow more efficient use of the NMR spectrometers. In working through the pulse optimization proble ms, the necessity of comparing experiment with theory on a regular basis became paramount. The best approach is to start by writing a simulation for a simple pulse sequence that needs optimizing. Next, run some

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153 experiments on the spectrometer and observe t he difference between the initial simulations and the experiment. Work on the experimental side until any discrepancies are minimal. Switch back to the simulations and try to make the simulations match the experiments. I found that this was usually where t he breakthroughs came. Once you have a model that accurately reproduces experimental data, the experiment can be modified to achieve what is actually desired, i.e. homogeneity improved, moving/changing where proton decoupling is on, etc, all the time makin g sure that an accurate simulation is maintained. Another area where constrained optimization may be better is to limit how long the final pulse sequence can be to some smaller value. The refocusing pulse sequences found here and elsewhere tend to be on the order of 7 times longer than a hard 180 pulse. It would be interesting to try to minimize that time while keeping the same broadband capabilities. The path for the next person working on optimizing pulse sequences should probably start by optimizing inve rsion pulse sequences. This provides a straightforward method for testing optimizations systems since the correlation between simulation and experiment is very good in this case. Once the optimization system/method is running well on inversion pulse sequen ces, move on to optimizing refocusing pulse sequences. The correlation between simulation and experiment diverges a bit more in this case, but is still quite good. Implementing the refocusing pulses in a more complicated pulse program reveals how well the whole system works. When both inversion and refocusing pulse sequence optimizations are running well, then the more complicated problem of interest should be tackled. This method will build up understanding of the whole process quickly so that problems wit h the more complicated pulse sequence optimization are more easily solved and understood. It might be even better to start by optimizing for liquids since the mathematics behind liquids is much simpler than solids. This

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154 would provide a basic understanding of what is going on mathematically much faster than starting with solids. In either case, it was very instructive for the author to write his own simulator for liquids simulations. Modifying them to solids might also have been instructive, but is hard to j ustify since several good simulators are already in existence. In the future it would be very interesting to explore spectrometer in the loop optimizations to see if there are better and faster ways to do this than have been presented in the literature so far. A combination of in silico and spectrometer in the loop optimization would probably generate the absolute best pulse sequences. It is possible to have the simulator try to match the current spectra exactly between each acquisition so that the optimiz ation scheme can make faster steps towards optimality rather than using only the data from the spectrometer.

161 hold all; grid on scatter(f/1000/pwr, xproj, 6, f/1000, 'filled') a = axis; axis([a(1) a(2) 1 1]) set(gca, 'fontsize', 16) xlabel(' \ omega_o_f_f_s_e_t/ \ omega_n_u_t_a_t_i_o_n', 'fontsize', 20) ylabel('I_Z Magnitude', 'fontsize', 20) if(p) print(' dpsc', append', plots_fname) end end Data Preparation Most of the processing functions and scripts used for this document expect that the data be in .mat files. The processed data should be in a file named expNN.mat where NN is the experiment number. For instance, the processed data for experiment 19 in the dataset MAS1208 is saved as exp19.mat in the folder MAS1208 under ~/Seth/750Data. The integrated data is saved as a separate file named expNNint.mat. The processing script named ndnmr_sam will generate these files after processing all data by pushing the Save Processed FIDs and Save Integration Data buttons. The data processing program that Neil Wargo has been working on saves the data in a different f ormat as processed_data.mat and integration_data.mat in the actual data folder. For example the data for experiment 99 in the dataset MAS1208 is saved as ~/Seth/750Data/MAS1208/99/processed_data.mat. I wrote a conversion function called long2ndnmr. Long2nd nmr.m function long2ndnmr(exps) % function long2ndnmr(exps) % % This function goes through the directories specified by the numbers in % exps loading processed_data.mat and integration_data.mat if they exist % and saving them as expXX.mat and expXXint.mat in the directory where the % function is called from. % 2009 January 01 % Seth McNeill data_fname = 'processed_data.mat'; int_fname = 'integration_data.mat' ; start_dir = pwd;

194 maxRamp 100 # maximum power percentage for ramp minRamp 50 # minimum power percentage for ramp nRamp 20 simulator_fname /Users/mcnese/apps/simpson # this is for etude #simulator_fname /usr/local/bin/simpson # this is for ascaris/briggsae #simulator_fname ~/bin/simpson # this is for hpc stdout_fname simpson_out.txt

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195 APPENDIX B OPTIMIZATION SCRIPTS Inversion Optimization create_run.sh This script creates the needed directories and runs an inversion optimization. The usage can be seen by running the script with no arguments. The run_fname is the name of the run file created by compiling the functions. This script does expect that the MCR files for running compiled Matlab code are located at: ~/bin/mcr/v78/v78. Running mcrinstaller in Matlab will show you where the binary file is located that will i nstall the mcr files. The mcr files must be installed for compiled Matlab to run. Useage: create_run.sh run_fname par_fname npulses #!/bin/bash # create_run.sh # # This file should write a submitable script to run an inversion optimization # and the submits it to the cluster. # # INPUTS: # run_fname the name of the compiled matlab script # par_fname name of the par file to use # npulses number of pulses to use in optimization # # Seth McNeill # 2008 June 20 if [ $# lt 3 ] # check to make sure there are at least 2 commandline inputs then echo "Useage: create_run.sh run_fname par_fname npulses" exit 1 fi run_fname=$1 par_fname=$2 npulses=$3 mat_prgm_fname=`echo $run_fname | sed 's/run_//' | sed 's/.sh//'` # grab the name base from the input file name_base=`grep "^name_base" $par_fname | awk '{ print $2 }'` if [ z "$name_base" ] then name_base="inv" fi # grab the maximum cpu time to use from the input file max_cpu_time=`grep "^max_cpu_time" $par_fname | awk '{ print $2 }'` # ch eck to see if more than one cpu is going to be used multicpu=`grep "^sim_opts" $par_fname | grep split` if [ n "$multicpu" ] then echo $multicpu echo "How many cores does this script use?" read ncpus else

243 BIOGRAPHICAL SKETCH Back in 1978, Seth McNeill was born third of four boys to James and Margaret McNeill. His first 15 years were spent in southern California halfwa y between Los Angeles and Palm Springs. He was home schooled through third grade, and went to the school where his older brothers were already in fourth grade. The teacher was worried that Seth would not sit still through a whole day of school, but somehow she managed to get him to do so. After his freshman year of high school, his family moved to Tri Cities in southeastern Washington state. Here Seth went to two more high schools before graduating from Upper Columbia Academy. Somewhere along the way it had become obvious that electrical engineering would be his major of pursuit having learned electronics from his older brother (now a mechanical engineer) who had learned it from his father. In his freshman year of college Seth started working for Ralph Stirl ing, the projects engineer, at Walla Walla College a job he continued throughout his college career, including some summers. This job provided good training in embedded systems. He enjoyed reading the datasheets of the parts he was supposed to enter into t he Mentor Graphics database. He also learned UNIX systems and was forced to learn vi, which is still his preferred UNIX editor. About March of his final year (he squeezed his 4 year degree down to 5 years somehow), he realized that to achieve his goal of t eaching electrical engineer at the collegiate level he would have to go to graduate school. It was already past application deadlines, so he asked the company he had interned and done his senior project for (Cadwell Laboratories) if they needed another ele ctrical engineer for a year. They agreed to it and Seth enjoyed a year living at home and working on low power, embedded system design for wearable, distributed medical monitoring. That job taught him the importance of understanding digital signal processi ng. When applying for graduate schools, Seth looked east with the thought that he could try out eastern living for a while and move back west when he was done. He applied to a few schools by

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244 January, but sometime in February he saw the micro air vehicle pr oject at the University of Florida advertised in the propaganda sheet that had been sent to his dad, who had done a fellowship at UF. That sparked his interest since he had been tinkering with robotics since seventh or eighth grade. Further exploration s howed that UF did not have a hard closing date for applications. He sent one to them late and with his most outlandish statement of purpose and he got in! Not only that, UF was the only school who offered any kind of financial support starting his first ye ar. After visiting and finding the faculty friendly and helpful and the church more so, he decided to attend UF. Seth did a nonthesis masters focusing on DSP, networking, and primarily artificial intelligence, pattern recognition, and image processing. W hen he left for an internship at Caltechs Jet Propulsion Lab the summer after he graduated with his masters, he planned to start his PhD under Dr. Michael Nechyba. Upon his return from his summer internships (he also worked a couple weeks at an aggregate packing plant engineering firm where he had worked the previous summer), he found that Dr. Nechyba had decided to move to industry. Dr. Arroyo was kind enough to take Seth on if he could find funding. Seth spent that fall semester visiting labs around cam pus that were working on projects that were interesting. Out of the blue one day, his friend OJ from church suggested that Seth take a short introductory course on nuclear magnetic resonance. Not knowing much more than that it involved large super conducti ng magnets and cryogens Seth agreed. During the last lab of the class, Dr. Longs postdoc, Dr. Mini Samuel -Landtiser asked what he did. Upon hearing that he was a programmer since coming to graduate school, she said that Dr. Long might be able to use his skills. An hour later he had an offer to join the lab where he completed his PhD. It has been a surprising path, but God has always been behind it making it work for the best.